The supersymmetric index in four dimensions

Abstract

We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples.

This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17 Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf

References in corpus (9)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Localization on Hopf surfaces
• SQCD: A Geometric Apercu
• Superconformal indices for N=1 theories with multiple duals
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• Localization on three-dimensional manifolds
• On the ISS model of dynamical SUSY breaking
• An introduction to supersymmetric field theories in curved space
• N=2 SUSY gauge theories on S^4

Cited by in corpus (43)

• Localization techniques in quantum field theories
• A 4d N=1 Cardy Formula
• EFT and the SUSY Index on the 2nd Sheet
• Rank $Q$ E-string on a torus with flux
• Localization on three-dimensional manifolds
• On the large R-charge $\mathcal{N}=2$ chiral correlators and the Toda equation
• Delayed Deconfinement and the Hawking-Page Transition
• Higher-Derivative Corrections and AdS${}_5$ Black Holes
• Gapped Chiral Fermions
• A slow review of the AGT correspondence
• 4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations
• Introduction to localization in quantum field theory
• An introduction to supersymmetric field theories in curved space
• An N=1 Lagrangian for an N=3 SCFT
• An N=1 Lagrangian for the rank 1 E6 superconformal theory
• Flavored surface defects in 4d N=1 SCFTs
• A brief review of the 2d/4d correspondences
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Curious patterns of IR symmetry enhancement
• Dualities from dualities: the sequential deconfinement technique
• Kaluza-Klein Spectroscopy for the Leigh-Strassler SCFT
• Topological Correlators and Surface Defects from Equivariant Cohomology
• Twisted characters and holomorphic symmetries
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• Symmetry enhancement and duality walls in 5d gauge theories
• Flowing from 16 to 32 Supercharges
• $\mathcal{N}=1$ conformal duals of gauged $E_n$ MN models
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Conformal S-dualities from O-planes
• Non minimal D-type conformal matter compactified on three punctured spheres
• A Nilpotency Index of Conformal Manifolds
• Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae
• The rarefied elliptic Bailey lemma and the Yang-Baxter equation
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Superconformal indices, Seiberg dualities and special functions
• Witten index for weak supersymmetric systems: invariance under deformations
• Rank $Q$ E-String on Spheres with Flux
• Wrapped M5-branes and AdS${}_5$ Black Holes
• Hawking-Page transition on a spin chain
• Weak supersymmetric $su(N|1)$ quantum systems
• Schur Connections: Chord Counting, Line Operators, and Indices
• Weak supersymmetry and superconformal indices
• Aspects of 4d supersymmetric dynamics and geometry