Calculating the Superconformal Index and Seiberg Duality

Abstract

We develop techniques to calculate an index for four dimensional superconformal field theories. This superconformal index is counting BPS operators which preserve only one supercharge. To calculate the superconformal index we quantize the field theory on S^3 X R and show that the twisted theory has an appropriate mass gap. This allows for the interactions to be switched off continuously without the superconformal index being changed. We test those techniques for theories which go through a non-trivial RG flow and for Seiberg dual theories. This leads to the conjecture of some group/number theoretical identities.

25 pages

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Cited by in corpus (64)

• 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
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• S-duality and 2d Topological QFT
• The Geometry of Supersymmetric Partition Functions
• 4d Index to 3d Index and 2d TQFT
• Localization on Hopf surfaces
• From 4d superconformal indices to 3d partition functions
• SQCD: A Geometric Apercu
• The Superconformal Index of the E_6 SCFT
• Relation between the 4d superconformal index and the S^3 partition function
• Superconformal indices of three-dimensional theories related by mirror symmetry
• The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
• A 4d N=1 Cardy Formula
• Superconformal indices for N=1 theories with multiple duals
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• An E7 Surprise
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• Comments on the Casimir energy in supersymmetric field theories
• Charting Class ${\mathcal{S}}_k$ Territory
• Superconformal indices of $\mathcal{N}=4$ SYM field theories
• Seiberg dualities and the 3d/4d connection
• Factorization of S^3/Z_n partition function
• Studying superconformal symmetry enhancement through indices
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• The star-triangle relation and 3d superconformal indices
• On the ISS model of dynamical SUSY breaking
• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• Supersymmetric dualities beyond the conformal window
• Vanishing superconformal indices and the chiral symmetry breaking
• New N=1 dualities from orientifold transitions - Part II: String Theory
• A new pentagon identity for the tetrahedron index
• Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS${}_5$
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• SU(2|2) supersymmetric mechanics
• A review on SUSY gauge theories on $S^3$
• Charging the Superconformal Index
• Superconformal indices and partition functions for supersymmetric field theories
• Phases of N=1 supersymmetric chiral gauge theories
• Mathematical structures behind supersymmetric dualities
• The Complete One-loop Spin Chain of N =1 SQCD
• Confinement and duality in supersymmetric gauge theories
• High-temperature asymptotics of the 4d superconformal index
• Lectures on 4d N=1 dynamics and related topics
• Integral pentagon relations for 3d superconformal indices
• Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Superconformal index of higher derivative $\mathcal{N}=1$ multiplets in four dimensions
• Standard Model Plethystics
• Index for Three Dimensional Superconformal Field Theories and Its Applications
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• Constraints on the R-charges of Free Bound States from the Römelsberger Index
• Is toric duality a Seiberg-like duality in (2+1)-d ?
• Witten index for weak supersymmetric systems: invariance under deformations
• Aspects of elliptic hypergeometric functions
• SU$(2|1)$ supersymmetric spinning models of chiral superfields
• Local Operators from the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Strongly coupled phases of $\mathcal{N}=1$ S-duality
• On the Superconformal Index of Chern-Simons theories and their KK Spectrometry
• On the Vacuum Structure of the 3-2 Model
• Variations of supersymmetric quantum mechanics and superconformal indices
• Weak supersymmetric $su(N|1)$ quantum systems
• Holography, Supergravity, and the Weak Gravity Conjecture