Holomorphic Blocks in Three Dimensions

Abstract

We decompose sphere partition functions and indices of three-dimensional N=2 gauge theories into a sum of products involving a universal set of "holomorphic blocks". The blocks count BPS states and are in one-to-one correspondence with the theory's massive vacua. We also propose a new, effective technique for calculating the holomorphic blocks, inspired by a reduction to supersymmetric quantum mechanics. The blocks turn out to possess a wealth of surprising properties, such as a Stokes phenomenon that integrates nicely with actions of three-dimensional mirror symmetry. The blocks also have interesting dual interpretations. For theories arising from the compactification of the six-dimensional (2,0) theory on a three-manifold M, the blocks belong to a basis of wavefunctions in analytically continued Chern-Simons theory on M. For theories engineered on branes in Calabi-Yau geometries, the blocks offer a non-perturbative perspective on open topological string partition functions.

124 pages, 21 figures. v3: Typos corrected

References in corpus (15)

• Exact Results in D=2 Supersymmetric Gauge Theories
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Comments on Chern-Simons Contact Terms in Three Dimensions
• Bootstrapping the superconformal index with surface defects
• Supersymmetry on Curved Spaces and Holography
• Exploring Curved Superspace
• Exact Kahler Potential from Gauge Theory and Mirror Symmetry
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Super-A-polynomial for knots and BPS states
• An E7 Surprise
• 3d analogs of Argyres-Douglas theories and knot homologies
• Refined Black Hole Ensembles and Topological Strings

Cited by in corpus (135)

• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• A topologically twisted index for three-dimensional supersymmetric theories
• Defects and Quantum Seiberg-Witten Geometry
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Dual Boundary Conditions in 3d SCFT's
• Supersymmetric partition functions and the three-dimensional A-twist
• The equivariant A-twist and gauged linear sigma models on the two-sphere
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Lectures on AdS Black Holes, Holography and Localization
• Nonsupersymmetric dualities from mirror symmetry
• Gluing gravitational blocks for AdS black holes
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• 5d Partition Functions with A Twist
• Factorisation and holomorphic blocks in 4d
• Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1\times D^2$
• The Cardy limit of the topologically twisted index and black strings in AdS${}_5$
• Localization on three-dimensional manifolds
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Rotating multi-charge spindles and their microstates
• Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks
• Universal 3d Cardy Block and Black Hole Entropy
• Rotating Black Hole Entropy from M5-branes
• Peacock patterns and new integer invariants in topological string theory
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• On matrix models and their $q$-deformations
• A slow review of the AGT correspondence
• ABJM on ellipsoid and topological strings
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• M-theoretic Genesis of Topological Phases
• Bootstrapping BPS spectra of 5d/6d field theories
• An elliptic Virasoro symmetry in 6d
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• 3d-3d Correspondence Revisited
• Boundaries, Vermas, and Factorisation
• From S-confinement to 3D Chiral Theories: Dressing the Monopoles
• From 3d duality to 2d duality
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• Teichmuller TQFT vs Chern-Simons Theory
• Large $N$ twisted partition functions in 3d-3d correspondence and Holography
• 3d-3d correspondence for mapping tori
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Sphere correlation functions and Verma modules
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Quiver gauge theories and integrable lattice models
• Higgsed network calculus
• $q$-Virasoro modular double and 3d partition functions
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• Exponential Networks, WKB and Topological String
• Chern-Simons theory from M5-branes and calibrated M2-branes
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• $\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
• Basic hypergeometry of supersymmetric dualities
• Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
• A 3d-3d appetizer
• Microstates of accelerating and supersymmetric AdS${}_4$ black holes from the spindle index
• Abelian dualities of $\mathcal{N}=(0,4)$ boundary conditions
• Ellipsoid partition function from Seiberg-Witten monopoles
• The resurgent structure of quantum knot invariants
• 3d Mirror Symmetry from S-duality
• Supersymmetric solutions and Borel singularities for N=2 supersymmetric Chern-Simons theories
• On 3d Seiberg-like Dualities with Two Adjoints
• Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $\mathcal{N}=2$ field theories
• Universal AdS black holes in theories with sixteen supercharges and their microstates
• Solving q-Virasoro constraints
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• Refined 3d-3d Correspondence
• 3d Expansions of 5d Instanton Partition Functions
• Modularity of supersymmetric partition functions
• Blocks and Vortices in the 3d ADHM Quiver Gauge Theory
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• The joy of factorization at large $N$: five-dimensional indices and AdS black holes
• Intersecting Defects and Supergroup Gauge Theory
• Wilson loop algebras and quantum K-theory for Grassmannians
• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
• Factorisation of 3d $\mathcal{N}=4$ Twisted Indices and the Geometry of Vortex Moduli Space
• Quantum K-Theory of Calabi-Yau Manifolds
• Factorising the 3D Topologically Twisted Index
• 1-efficient triangulations and the index of a cusped hyperbolic 3-manifold
• AdS2/CFT1, Whittaker vector and Wheeler-De Witt equation
• Superconformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ and mirror symmetry
• SYM on Quotients of Spheres and Complex Projective Spaces
• BPS Indices, Modularity and Perturbations in Quantum K-theory
• Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories
• Abelian 3d mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ with $N_f=1$
• Elliptic modular double and 4d partition functions
• On Supersymmetry, Boundary Actions and Brane Charges
• Trinion Conformal Blocks from Topological strings
• Infrared phases of 3D Class R theories
• Knots, Perturbative Series and Quantum Modularity
• The ABCDEFG of Little Strings
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Marginal Deformations of 3d N=4 Linear Quiver Theories
• Seiberg-like dualities for orthogonal and symplectic 3d $\mathcal{N}=2$ gauge theories with boundaries
• Gromov-Witten invariants and localization
• Gauge origami and quiver W-algebras
• Knots and Their Related $q$-Series
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks
• BPS States Meet Generalized Cohomology
• Conformal Quantum Mechanics, Holomorphic Factorisation, and Ultra-Spinning Black Holes
• Abelian mirror symmetry of $\mathcal{N}=(2,2)$ boundary conditions
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• Localization and Non-Renormalization in Chern-Simons Theory
• (0,2) Dualities and the 4-Simplex
• Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory
• Monopole deformations of 3d Seiberg-like dualities with adjoint matters
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• A Geometric Quantisation view on the AJ-conjecture for the Teichmüller TQFT
• Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N}=2$ theories
• From equivariant volumes to equivariant periods
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities
• Supersymmetric Wilson Loops, Instantons, and Deformed $\mathcal{W}$-Algebras
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• On the Quantum K-Theory of the Quintic
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
• Varieties of Abelian mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$
• Virasoro Constraint for Uglov Matrix Model
• $\mathcal{I}$-extremization with baryonic charges
• The colored Jones polynomials as vortex partition functions
• Line defect half-indices of $SU(N)$ Chern-Simons theories
• 3D-3D Correspondence from Seifert Fibering Operators
• Resurgence in complex Chern-Simons theory at generic levels
• N=2 Chern-Simons-Matter Theories Without Vortices
• Stokes Phenomena in 3d $\mathcal{N}=2$ SQED${}_2$ and ${\mathbb{CP}}^1$ Models
• Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle
• Schur Connections: Chord Counting, Line Operators, and Indices
• Partition functions for supersymmetric gauge theories on spheres