BPS Degeneracies and Superconformal Index in Diverse Dimensions

Abstract

We present a unifying theme relating BPS partition functions and superconformal indices. In the case with complex SUSY central charges (as in N=2 in d=4 and N=(2,2) in d=2) the known results can be reinterpreted as the statement that the BPS partition functions can be used to compute a specialization of the superconformal indices. We argue that in the case with real central charge in the supersymmetry algebra, as in N=1 in d=5 (or the N=2 in d=3), the BPS degeneracy captures the full superconformal index. Furthermore, we argue that refined topological strings, which captures 5d BPS degeneracies of M-theory on CY 3-folds, can be used to compute 5d supersymmetric index including in the sectors with 3d defects for a large class of 5d superconformal theories. Moreover, we provide evidence that distinct Calabi-Yau singularities which are expected to lead to the same SCFT yield the same index.

58 pages

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Cited by in corpus (59)

• M-Strings
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• Three dimensional canonical singularity and five dimensional N=1 SCFT
• Topological strings and 5d T_N partition functions
• Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
• Surface Defects and Chiral Algebras
• Surface Defects and Resolvents
• Discrete theta and the 5d superconformal index
• Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories
• Brane webs and $O5$-planes
• Fiber-Base Duality and Global Symmetry Enhancement
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Chiral algebra of Argyres-Douglas theory from M5 brane
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Tao Probing the End of the World
• Magnetic Quivers from Brane Webs with O5 Planes
• On Irregular Singularity Wave Functions and Superconformal Indices
• Instantons, Symmetries and Anomalies in Five Dimensions
• E + E $\to$ H
• Macdonald Index and Chiral Algebra
• Holomorphic blocks and the 5d AGT correspondence
• Exact partition functions of Higgsed 5d $T_N$ theories
• Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM
• Bootstrapping BPS spectra of 5d/6d field theories
• Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers
• An elliptic Virasoro symmetry in 6d
• Surface Defect Indices and 2d-4d BPS States
• Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions
• Holomorphic Blocks for 3d Non-abelian Partition Functions
• On the 5d instanton index as a Hilbert series
• On AGT-W Conjecture and q-Deformed W-Algebra
• $q$-Virasoro modular double and 3d partition functions
• On the BPS spectrum of 5d SU(2) super-Yang-Mills
• The refined BPS index from stable pair invariants
• Notes on Enhancement of Flavor Symmetry and 5d Superconformal Index
• Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills
• BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations
• The 5d Superconformal Index at Large $N$ and Black Holes
• Refined Topological Strings on Local ${\mathbb{P}}^2$
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Elliptic modular double and 4d partition functions
• Trinion Conformal Blocks from Topological strings
• Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories
• Superconformal Index, BPS Monodromy and Chiral Algebras
• Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I
• Factorization of the 3d superconformal index
• An infrared bootstrap of the Schur index with surface defects
• Weyl invariant Jacobi forms along Higgsing trees
• $Y$ systems, $Q$ systems, and 4D $\mathcal{N}=2$ supersymmetric QFT
• Quantum Geometry and $\theta$-Angle in Five-Dimensional Super Yang-Mills
• The NS limit of the 5D Superconformal Index
• A Family of Vertex Algebras from Argyres-Douglas Theory
• Proving the 6d Cardy Formula and Matching Global Gravitational Anomalies