An Index for 4 dimensional Super Conformal Theories

Abstract

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3\times$ time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the $\mathcal{N}=4$ theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $Ad{S}_5\times S^5$ and find perfect agreement at large $N$ and small charges. Our index does not reproduce the entropy of supersymmetric black holes in $Ad{S}_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the $\mathcal{N}=4$ theory. We note that entropy for some small supersymmetric $Ad{S}_5$ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the $\mathcal{N}=4$ Yang Mills theory.

harvmac 40+16 pages, v3: references and table of contents added, typos fixed

References in corpus (12)

• General Non-Extremal Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity
• Fivebranes from gauge theory
• A first order deconfinement transition in large N Yang-Mills theory on a small 3-sphere
• Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle
• Large N BPS states and emergent quantum gravity
• Finite temperature effective action, AdS_5 black holes, and 1/N expansion
• The Phase Structure of Low Dimensional Large N Gauge Theories on Tori
• R-charged AdS_{5} black holes and large N unitary matrix models
• Current Correlators and AdS/CFT Geometry
• Fine structure of Hagedorn transitions
• Operator mixing in N=4 SYM: The Konishi anomaly revisited
• Higher spin holography for SYM in d dimensions

Cited by in corpus (546)

• Black Holes in Higher Dimensions
• Infinite Chiral Symmetry in Four Dimensions
• Rigid Supersymmetric Theories in Curved Superspace
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Gauge Theories and Macdonald Polynomials
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• The complete superconformal index for N=6 Chern-Simons theory
• Counting Gauge Invariants: the Plethystic Program
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• 3d dualities from 4d dualities
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• S-duality and 2d Topological QFT
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Classification of near-horizon geometries of extremal black holes
• Supersymmetric multi-charge AdS_5 black holes
• Bootstrapping the superconformal index with surface defects
• Kerr-AdS/CFT Correspondence in Diverse Dimensions
• Holomorphic Blocks in Three Dimensions
• M5-branes from gauge theories on the 5-sphere
• The Geometry of Supersymmetric Partition Functions
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• Supersymmetry on Curved Spaces and Holography
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
• Comments on twisted indices in 3d supersymmetric gauge theories
• 2d Index and Surface operators
• Black Holes as Effective Geometries
• Black hole thermodynamics from simulations of lattice Yang-Mills theory
• Deformations of Superconformal Theories
• Localization on Hopf surfaces
• Correlation Functions of Coulomb Branch Operators
• 4d Index to 3d Index and 2d TQFT
• N=1 Deformations and RG Flows of N=2 SCFTs
• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• From 4d superconformal indices to 3d partition functions
• The $\mathcal{N}=2$ superconformal bootstrap
• Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• On the Superconformal Index of Argyres-Douglas Theories
• Elliptic hypergeometry of supersymmetric dualities
• 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory
• On instantons as Kaluza-Klein modes of M5-branes
• Knot Homology from Refined Chern-Simons Theory
• Brane Tilings and Their Applications
• Supersymmetric states of N=4 Yang-Mills from giant gravitons
• Three-dimensional N=6 SCFT's and their membrane dynamics
• A non-renormalization theorem for chiral primary 3-point functions
• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• The Superconformal Index of the E_6 SCFT
• Diagonal free field matrix correlators, global symmetries and giant gravitons
• Relation between the 4d superconformal index and the S^3 partition function
• Supersymmetric Index from Black Hole Entropy
• Superconformal indices of three-dimensional theories related by mirror symmetry
• The asymptotic growth of states of the 4d N=1 superconformal index
• Dual Boundary Conditions in 3d SCFT's
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• Coulomb Branch and The Moduli Space of Instantons
• The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
• The BPS limit of rotating AdS black hole thermodynamics
• Tinkertoys for the Twisted D-Series
• A 4d N=1 Cardy Formula
• Exceptional Indices
• Superconformal indices for N=1 theories with multiple duals
• Instantons on the 5-sphere and M5-branes
• Calculating the Superconformal Index and Seiberg Duality
• M5-branes, toric diagrams and gauge theory duality
• Counting Chiral Operators in Quiver Gauge Theories
• Lectures on AdS Black Holes, Holography and Localization
• Entropy function and attractors for AdS black holes
• Surface Defects and Chiral Algebras
• BPS Degeneracies and Superconformal Index in Diverse Dimensions
• Counting BPS operators in N=4 SYM
• The superconformal index of N=1 class S fixed points
• Discrete theta and the 5d superconformal index
• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• Infrared Computations of Defect Schur Indices
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• Recursion Relations for AdS/CFT Correlators
• Towards lattice simulation of the gauge theory duals to black holes and hot strings
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• Fiber-Base Duality and Global Symmetry Enhancement
• Braids, Walls, and Mirrors
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• BCFW for Witten Diagrams
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• Comments on 1/16 BPS Quantum States and Classical Configurations
• EFT and the SUSY Index on the 2nd Sheet
• Extremal Static AdS Black Hole/CFT Correspondence in Gauged Supergravities
• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• Lifting 4d dualities to 5d
• An E7 Surprise
• T^σ_ρ(G) Theories and Their Hilbert Series
• E-String Theory on Riemann Surfaces
• Gluing gravitational blocks for AdS black holes
• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• Chiral Algebras for Trinion Theories
• 5d Partition Functions with A Twist
• VOAs labelled by complex reflection groups and 4d SCFTs
• High-temperature asymptotics of supersymmetric partition functions
• Supersymmetric Casimir Energy and the Anomaly Polynomial
• Extracting black hole physics from the lattice
• Duality and enhancement of symmetry in 5d gauge theories
• Supersymmetric phases of 4d N=4 SYM at large N
• The exact Schur index of $\mathcal{N}=4$ SYM
• Asymptotic growth of the 4d $\mathcal{N}=4$ index and partially deconfined phases
• 3-Manifolds and 3d Indices
• N=4 Superconformal Characters and Partition Functions
• CFT Duals for Attractor Horizons
• Reducing the 4d Index to the S^3 Partition Function
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• The supersymmetric index in four dimensions
• Line Operator Index on S1 $\times$ S3
• A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index
• Compactification of 6d minimal SCFTs on Riemann surfaces
• A Fermi Surface Model for Large Supersymmetric AdS_5 Black Holes
• Dual Giant Gravitons in Sasaki-Einstein Backgrounds
• Holographic renormalization and supersymmetry
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions
• Hilbert Series for Moduli Spaces of Two Instantons
• AdS black holes and finite N indices
• Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• Surprisingly Simple Spectra
• Brane Effective Actions, Kappa-Symmetry and Applications
• Superconformal indices at large $N$ and the entropy of AdS${}_5$ $\times$ SE${}_5$ black holes
• Words to describe a black hole
• Superconformal surfaces in four dimensions
• Rank $Q$ E-string on a torus with flux
• 1/16 BPS States in N=4 SYM
• Index for Orbifold Quiver Gauge Theories
• Entropy of near-extremal black holes in AdS_5
• Constraints on Chiral Operators in N=2 SCFTs
• Near-horizon geometries of supersymmetric AdS(5) black holes
• Compactifications of ADE conformal matter on a torus
• A Critique of the Fuzzball Program
• 5d/6d DE instantons from trivalent gluing of web diagrams
• A Bethe Ansatz type formula for the superconformal index
• Argyres-Douglas Theories, S^1 Reductions, and Topological Symmetries
• The Superconformal Index of Class S Theories of Type D
• Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• $\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
• Localization on three-dimensional manifolds
• S-duality and the N=2 Lens Space Index
• Tri-vertices and SU(2)'s
• Rigid supersymmetric theories in 4d Riemannian space
• Corrections to AdS${}_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity
• Quivers, YBE and 3-manifolds
• Operator Dimensions from Moduli
• A review of the T_N theory and its cousins
• Tinkertoys for the Z3-twisted D4 Theory
• Nonrelativistic Superconformal M2-Brane Theory
• Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index
• Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
• Quivers as Calculators: Counting, Correlators and Riemann Surfaces
• Macdonald Index and Chiral Algebra
• The Veneziano Limit of N=2 Superconformal QCD: Towards the String Dual of N=2 SU(N_c) SYM with N_f =2 N_c
• 2d TQFT structure of the superconformal indices with outer-automorphism twists
• Delayed Deconfinement and the Hawking-Page Transition
• High-Temperature Expansion of Supersymmetric Partition Functions
• The Superconformal Index of the (2,0) Theory with Defects
• A note on the entropy of rotating BPS AdS${}_7\times S^4$ black holes
• The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
• On Exceptional Instanton Strings
• Higher-Derivative Corrections and AdS${}_5$ Black Holes
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• Schur index of the $\mathcal{N}=4$ $U(N)$ SYM via the AdS/CFT correspondence
• Aspects of Superconformal Multiplets in D>4
• Black hole entropy function for toric theories via Bethe Ansatz
• From counting to construction of BPS states in N=4 SYM
• Entropy function from toric geometry
• On Superconformal Characters and Partition Functions in Three Dimensions
• 5d superconformal indices at large N and holography
• Duality walls and defects in 5d N=1 theories
• Charting Class ${\mathcal{S}}_k$ Territory
• Superconformal indices of $\mathcal{N}=4$ SYM field theories
• Central Charges of 2d Superconformal Defects
• On a modular property of N=2 superconformal theories in four dimensions
• Long Multiplet Bootstrap
• Supersymmetric SYK models
• The superconformal index and an elliptic algebra of surface defects
• The gravity dual of supersymmetric gauge theories on a squashed $S^1\times S^3$
• A Duality Appetizer
• Finite $N$ Corrections to the Superconformal Index of S-fold Theories
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
• Gapped Chiral Fermions
• Baryonic Generating Functions
• Free Fermions and Thermal AdS/CFT
• Emergent 3-manifolds from 4d Superconformal Indices
• Higher Derivative Corrections and Central Charges from Wrapped M5-branes
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Network and Seiberg Duality
• Cardy Formula for 4d SUSY Theories and Localization
• Schur correlation functions on $S^3\times S^1$
• N=1 conformal dualities
• Counting Giant Gravitons in AdS_3
• The general M5-brane superconformal index
• Studying superconformal symmetry enhancement through indices
• The $\mathcal{N}=2$ Schur index from free fermions
• Invariant Differential Operators for Non-Compact Lie Algebras Parabolically Related to Conformal Lie Algebras
• From 6d flows to 4d flows
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• On S-duality of the Superconformal Index on Lens Spaces and 2d TQFT
• Surface defects, the superconformal index and q-deformed Yang-Mills
• Surface defects and elliptic quantum groups
• Finite-$N$ corrections to the M-brane indices
• The star-triangle relation and 3d superconformal indices
• Surface Defect Indices and 2d-4d BPS States
• Superconformal Index with Duality Domain Wall
• Phase Transitions of Large N Orbifold Gauge Theories
• AdS${}_5$ Black Hole Entropy near the BPS Limit
• On the ISS model of dynamical SUSY breaking
• Weakly Renormalized Near 1/16 SUSY Fermi Liquid Operators in N = 4 SYM
• Evidence for the existence of a novel class of supersymmetric black holes with AdS${}_5\times$S${}^5$ asymptotics
• Tinkertoys for the E7 Theory
• Linear Quivers and N=1 SCFTs from M5-branes
• Holography of BPS surface operators
• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
• Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge Theory
• AdS${}_7$ Black-Hole Entropy and 5D $\mathcal{N}=2$ Yang-Mills
• The exact Schur index in closed form
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• New Directions in Bipartite Field Theories
• Landscape of Simple Superconformal Field Theories in 4d
• $\mathcal{N}=2^{\ast }$ Schur indices
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• From S-confinement to 3D Chiral Theories: Dressing the Monopoles
• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• New Integrable Models from the Gauge/YBE Correspondence
• Supersymmetric Rényi entropy and charged hyperbolic black holes
• Vanishing superconformal indices and the chiral symmetry breaking
• Supersymmetric States in Large N Chern-Simons-Matter Theories
• Supersymmetric dualities beyond the conformal window
• N=1 theories of class S_k
• $c-a$ from the $N=1$ superconformal index
• N=4 SYM on S^3 with Near Critical Chemical Potentials
• Rotating Hairy Black Holes in AdS${}_5\times$S${}^5$
• Exact Stringy Microstates from Gauge Theories
• Probing the Higgs branch of 5d fixed point theories with dual giant gravitons in AdS(6)
• Supersymmetric States in M5/M2 CFTs
• Ungauging black holes and hidden supercharges
• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
• Decoding stringy near-supersymmetric black holes
• Central charges from the $\mathcal{N}=1$ superconformal index
• Gravitational Cardy Limit and AdS Black Hole Entropy
• Cut-and-join operators and N=4 super Yang-Mills
• 4d $\mathcal{N}=3$ indices via discrete gauging
• 4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations
• Crystal Melting and Wall Crossing Phenomena
• BPS Chaos
• New N=1 dualities from orientifold transitions - Part II: String Theory
• New N=1 dualities from orientifold transitions - Part I: Field Theory
• Symmetries of massless vertex operators in AdS(5) x S(5)
• Supergravitons from one loop perturbative N=4 SYM
• Dual giant gravitons in AdS${}_m$ $\times$ Y${}^n$ (Sasaki-Einstein)
• Quarter BPS classified by Brauer algebra
• Sphere correlation functions and Verma modules
• Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery
• Elliptic hypergeometric sum/integral transformations and supersymmetric lens index
• Aspects of Non-Relativistic Quantum Field Theories
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• An introduction to supersymmetric field theories in curved space
• Superconformal index of low-rank gauge theories via the Bethe Ansatz
• Quiver gauge theories and integrable lattice models
• 5D Black Holes and Non-linear Sigma Models
• Finite $N$ corrections to the superconformal index of toric quiver gauge theories
• Spin Chains in N=2 Superconformal Theories: from the Z_2 Quiver to Superconformal QCD
• Chern-Simons and RG Flows: Contact with Dualities
• An N=1 Lagrangian for an N=3 SCFT
• Stringy corrections to the entropy of electrically charged supersymmetric black holes with ${\mathrm{AdS}}_5\times S^5$ asymptotics
• $q$-Virasoro modular double and 3d partition functions
• An N=1 Lagrangian for the rank 1 E6 superconformal theory
• Partial-Symmetry-Breaking Phase Transitions
• Large $N$ Superconformal Indices for 3d Holographic SCFTs
• A new pentagon identity for the tetrahedron index
• 't Hooft anomalies and the holomorphy of supersymmetric partition functions
• Aspects of monopole operators in N=6 Chern-Simons theory
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• The $\mathcal{N}=4$ Schur index with Polyakov loops
• Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions
• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• Superconformal index for large N quiver Chern-Simons theories
• Extremal black holes, Holography & Coarse graining
• Interacting Giant Gravitons from Spin Matrix Theory
• Factorization of 4d N=1 superconformal index
• Exact QFT duals of AdS black holes
• Flavored surface defects in 4d N=1 SCFTs
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• On Melonic Supertensor Models
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• EFT Asymptotics: the Growth of Operator Degeneracy
• Supersymmetric Giant Graviton Solutions in AdS_3
• Basic hypergeometry of supersymmetric dualities
• Finite $N$ corrections to the superconformal index of orbifold quiver gauge theories
• Line defect Schur indices, Verlinde algebras and $U(1{)}_r$ fixed points
• A brief review of the 2d/4d correspondences
• Supersymmetric index on T^2 x S^2 and elliptic genus
• A Family of $4D$ $\mathcal{N}=2$ Interacting SCFTs from the Twisted $A_{2N}$ Series
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Vanishing OPE Coefficients in 4d N=2 SCFTs
• Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS${}_5$
• Monopole Quivers and new 3D N=2 dualities
• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• Dualities of Corner Configurations and Supersymmetric Indices
• S-duality in $\mathcal{N}=1$ orientifold SCFTs
• Weakly coupled conformal manifolds in 4d
• Surface defects in E-string compactifications and the van Diejen model
• Curious patterns of IR symmetry enhancement
• Superconformal Indices for Orbifold Chern-Simons Theories
• Exact Deconstruction of the 6D (2,0) Theory
• Finite $N$ indices and the giant graviton expansion
• Bulk geometry in gauge/gravity duality and color degrees of freedom
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• Higgs, Coulomb, and Hall-Littlewood
• Mirror symmetry of 3d $\mathcal{N}=4$ gauge theories and supersymmetric indices
• Euclidean analysis of the entropy functional formalism
• Dualities from dualities: the sequential deconfinement technique
• Surface defects as transfer matrices
• Between symmetry and duality in supersymmetric QFT
• Rethinking mirror symmetry as a local duality on fields
• Discrete gauging and Hasse diagrams
• Strings on conifolds from strong coupling dynamics, part I
• E3-brane instantons and baryonic operators for D3-branes on toric singularities
• On 3d Seiberg-like Dualities with Two Adjoints
• BPS Partition Functions for Quiver Gauge Theories: Counting Fermionic Operators
• Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills
• 4D and 2D superconformal index with surface operator
• Counting Wobbling Dual-Giants
• Large $N$ and large representations of Schur line defect correlators
• Kaluza-Klein Spectroscopy for the Leigh-Strassler SCFT
• Extended global symmetries for 4d N=1 SQCD theories
• Surface defects, flavored modular differential equations and modularity
• Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d
• Holonomy Saddles and Supersymmetry
• Probing the EVH limit of supersymmetric AdS black holes
• Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography
• A review on SUSY gauge theories on $S^3$
• Maximally twisted eleven-dimensional supergravity
• Holomorphic field theories and Calabi--Yau algebras
• State-space Manifold and Rotating Black Holes
• Superconformal index of N=3 orientifold theories
• Black Hole Entropy from Quantum Mechanics
• Star shaped quivers with flux
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• The 5d Superconformal Index at Large $N$ and Black Holes
• Charging the Superconformal Index
• Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM
• Flips, dualities and symmetry enhancements
• Symmetry enhancement and duality walls in 5d gauge theories
• E_8 orbits of IR dualities
• Universal Features of Four-Dimensional Superconformal Field Theory on Conic Space
• The Panorama of Spin Matrix Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Squashing the Boundary of Supersymmetric AdS${}_5$ Black Holes
• Microscopic Entropy of AdS${}_3$ Black Holes Revisited
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• An Index for Ray Operators in 5d $E_n$ SCFTs
• $\mathcal{N}=1$ conformal duals of gauged $E_n$ MN models
• String theory and the 4D/3D reduction of Seiberg duality. A Review
• Supersymmetric Casimir Energy and $\mathrm{SL}(3,\mathbb{Z})$ Transformations
• Finite N Index and Angular Momentum Bound from Gravity
• Quarter-BPS states, multi-symmetric functions and set partitions
• Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons
• Superconformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ and mirror symmetry
• T-Reflection
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Black hole microstates and supersymmetric localization
• Integrable lattice spin models from supersymmetric dualities
• Phase transitions and statistical mechanics for BPS Black Holes in AdS/CFT
• Star shaped quivers in four dimensions
• Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter
• Elliptic modular double and 4d partition functions
• The growth of the $\frac{1}{16}$-BPS index in 4d $\mathcal{N}=4$ SYM
• Small Black holes vs horizonless solutions in AdS
• Superconformal index with surface defects for class ${\mathcal{S}}_k$
• The shortened KK spectrum of IIB supergravity on Y^{p,q}
• Mathematical structures behind supersymmetric dualities
• Master Space and Hilbert Series for N=1 Field Theories
• Infinitely many N=1 dualities from $m+1-m=1$
• 4D, N=1 Supergravity Genomics
• Non minimal D-type conformal matter compactified on three punctured spheres
• Giant graviton expansions and ETW brane
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
• Conformal S-dualities from O-planes
• The Phase Diagram of BPS Black Holes in AdS${}_5$
• The giant graviton expansion in $Ad{S}_5\times S^5$
• Excitations of bubbling geometries for line defects
• BPS Partition Functions for S-folds
• A duality web of linear quivers
• Cardy Limits of 6d Superconformal Theories
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• Twisted Sectors in Gravity Duals of N=4 Chern-Simons Theories
• A freely generated ring for N=1 models in class S_k
• Closed form fermionic expressions for the Macdonald index
• Phase Transitions of Charged Kerr-AdS Black Holes from Large-N Gauge Theories
• The Romelsberger Index, Berkooz Deconfinement, and Infinite Families of Seiberg Duals
• From multi-gravitons to Black holes: The role of complex saddles
• Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• A Nilpotency Index of Conformal Manifolds
• Superconformal Index, BPS Monodromy and Chiral Algebras
• 5D SYM on 3D Deformed Spheres
• Integral identities for 3d dualities with SP(2N) gauge groups
• Correlations vs connectivity in R-charge
• Emergent N=4 supersymmetry from N=1
• SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling
• 3d SUSY enhancement and non-semisimple TQFTs from four dimensions
• Branes and integrable lattice models
• Super-Yang-Mills theories on S4 x R
• Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies
• Supersymmetric Grey Galaxies, Dual Dressed Black Holes and the Superconformal Index
• Conformal Quantum Mechanics, Holomorphic Factorisation, and Ultra-Spinning Black Holes
• Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae
• The large-$N$ limit of 4d superconformal indices for general BPS charges
• Abelian mirror symmetry of $\mathcal{N}=(2,2)$ boundary conditions
• High-temperature asymptotics of the 4d superconformal index
• Integral pentagon relations for 3d superconformal indices
• N=1 Duality and the Superconformal Index
• 3d superconformal indices and isomorphisms of M2-brane theories
• Dyon dynamics near marginal stability and non-BPS states
• 1/2 BPS Correlator and Free Fermion
• No go for a flow
• Modified elliptic gamma functions and 6d superconformal indices
• The superconformal index of $\mathcal{N}=4$ $USp(2N_c)$ and $SO(N_c)$ SYM as a matrix integral
• Macdonald Indices for Four-dimensional $\mathcal{N}=3$ Theories
• General Supersymmetric AdS${}_5$ Black Holes with Squashed Boundary
• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence
• Root of unity asymptotics for Schur indices of 4d Lagrangian theories
• An infrared bootstrap of the Schur index with surface defects
• Entanglement in Theory Space
• An Index for Quantum Integrability
• Introduction to the theory of elliptic hypergeometric integrals
• Webs of 3d $\mathcal{N}=2$ dualities with D-type superpotentials
• Superconformal index of higher derivative $\mathcal{N}=1$ multiplets in four dimensions
• Deconstructing Defects
• Lessons from the Vacuum Structure of 4d N=2 Supergravity
• Fortuity and Supergravity
• Superconformal Quantum Mechanics on Kähler Cones
• Black holes and Large $N$ complex saddles in 3D-3D correspondence
• On Uniqueness of supersymmetric Black holes in AdS(5)
• Singularity, Sasaki-Einstein manifold, Log del Pezzo surface and $\mathcal{N}=1$ AdS/CFT correspondence: Part I
• Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement
• Laplace operators on Sasaki-Einstein manifolds
• Interpreting multiple dualities conjectured from superconformal index identities
• Index for Three Dimensional Superconformal Field Theories and Its Applications
• Surface defects and instanton partition functions
• The NS limit of the 5D Superconformal Index
• S-duality in the Cardy-like limit of the superconformal index
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• Electrovacuum Near-horizon Geometries in Four and Five Dimensions
• Distinquishing 4d N=2 SCFTs
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• From Gauss Graphs to Giants
• On topological field theory representation of higher analogs of classical special functions
• Equivalence of A-Maximization and Volume Minimization
• A Family of Vertex Algebras from Argyres-Douglas Theory
• Is toric duality a Seiberg-like duality in (2+1)-d ?
• Interactions as conformal intertwiners in 4D QFT
• Constraints on the R-charges of Free Bound States from the Römelsberger Index
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Superconformal indices, Seiberg dualities and special functions
• More on BPS States in N=4 Supersymmetric Yang-Mills Theory on R x S3
• BPS states and their reductions
• Kutasov-Seiberg dualities and cyclotomic polynomials
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• The Giant Graviton Expansion
• Finite-$N$ superconformal index via the AdS/CFT correspondence
• From $\beta$ to $\eta$: a new cohomology for deformed Sasaki-Einstein manifolds
• Quantum entropy of supersymmetric black holes
• A journey to 3d: exact relations for adjoint SQCD from dimensional reduction
• Integrability As Duality: The Gauge/YBE Correspondence
• Witten index for weak supersymmetric systems: invariance under deformations
• Orbifold Schur Index and IR formula
• Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins
• 4d/3d reduction of s-confining theories: the role of the "exotic" D instantons
• Thermodynamics of BPS and Near-BPS AdS6 Black Holes
• 4d $\mathcal{N}=1$ quiver gauge theories and the ${\mathrm{A}}_{\mathrm{n}}$ Bailey lemma
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Supersymmetric Electromagnetic Waves on Giants and Dual-Giants
• Rank $Q$ E-String on Spheres with Flux
• Lens space index and global properties for 4d N = 2 models
• Proving the 6d Cardy Formula and Matching Global Gravitational Anomalies
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• On Toda Equation and Half BPS Supergravity Solution in M-Theory
• $\mathcal{N}=2$ Argyres-Douglas theories, $\mathcal{N}=1$ SQCD and Seiberg duality
• Towards a Holographic Dual of SQCD: Holographic Anomalies and Higher Derivative Gravity
• Product SCFTs for the $E_7$ Theory
• Aspects of elliptic hypergeometric functions
• Confinement and XSB in QCD: Mysteries and beauty of soliton dynamics in nonAbelian gauge theories
• Local Operators from the Space of Vacua of Four Dimensional SUSY Gauge Theories
• $N^2$ entropy of 4D N=4 SYM
• On the Superconformal Index of Chern-Simons theories and their KK Spectrometry
• Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary
• All separable supersymmetric AdS${}_5$ black holes
• Witten index of BMN matrix quantum mechanics
• Generalized symmetry constraints on deformed 4d (S)CFTs
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail
• Strongly coupled phases of $\mathcal{N}=1$ S-duality
• Semi-classical monopole operators in Chern-Simons-matter theories
• The Null Decomposition of Conformal Algebras
• Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing
• Hawking-Page transition on a spin chain
• Superconformal Indices and M2-Branes
• Theories of Class S and New N=1 SCFTs
• On timelike supersymmetric solutions of Abelian gauged 5-dimensional supergravity
• The Weyl Anomaly from the 6D Superconformal Index
• On Poisson geometry and supersymmetric sigma models
• Symmetry structure of the interactions in near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory
• Index calculation by means of harmonic expansion
• Universal fine grained asymptotics of free and weakly coupled Quantum Field Theory
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Supersymmetric zeta functions and determinants
• A study of N =1 SCFT derived from N =2 SCFT: index and chiral ring
• Explicit Character Formulae for Positive Energy UIRs of D=4 Conformal Supersymmetry
• Supersymmetry in Hadron Spectroscopy and Solitons in 2 Dimensional Fermionic Media
• Classification of Invariant Differential Operators for Non-Compact Lie Algebras via Parabolic Relations
• The M2/M5 BPS Partition Functions from Supergravity
• Revisiting a family of five-dimensional charged, rotating black holes
• Off-shell phase diagram of BPS black holes in AdS${}_5$
• Schur Connections: Chord Counting, Line Operators, and Indices
• A Charge Constraint in BMN
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs
• Variations of supersymmetric quantum mechanics and superconformal indices
• Holographic spectral functions for Sasaki-Einstein 5-manifolds
• Quarter-indices for basic ortho-symplectic corners
• Weak supersymmetry and superconformal indices
• Classical probes for 1/16 SUSY operators
• Superconformal blocks for stress-tensor and chiral operators for 4D $\mathcal{N}=2$ superconformal field theories
• OPE of line defects in 5d $E_n$ SCFT
• Aspects of 4d supersymmetric dynamics and geometry
• 4D/3D reduction of dualities: mirrors on the circle
• Weak supersymmetric $su(N|1)$ quantum systems
• Holography, Supergravity, and the Weak Gravity Conjecture
• Vanishing short multiplets in rank one 4d/5d SCFTs
• Superconformal Index for $\mathcal{N}=3$ $\widehat{ADE}$ Chern-Simons Quiver Gauge Theories