EFT and the SUSY Index on the 2nd Sheet

Abstract

The counting of BPS states in four-dimensional $\mathcal{N}=1$ theories has attracted a lot of attention in recent years. For superconformal theories, these states are in one-to-one correspondence with local operators in various short representations. The generating function for this counting problem has branch cuts and hence several Cardy-like limits, which are analogous to high-temperature limits. Particularly interesting is the second sheet, which has been shown to capture the microstates and phases of supersymmetric black holes in AdS${}_5$. Here we present a 3d Effective Field Theory (EFT) approach to the high-temperature limit on the second sheet. We use the EFT to derive the behavior of the index at orders ${\beta }^{-2},{\beta }^{-1},{\beta }^0$. We also make a conjecture for $O(\beta )$, where we argue that the expansion truncates up to exponentially small corrections. An important point is the existence of vector multiplet zero modes, unaccompanied by massless matter fields. The runaway of Affleck-Harvey-Witten is however avoided by a non-perturbative confinement mechanism. This confinement mechanism guarantees that our results are robust.

43 pages; v2: minor corrections, clarifications added, references added

References in corpus (18)

• Generalized Global Symmetries
• Conformal collider physics: Energy and charge correlations
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Mirrors of 3d Sicilian theories
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Localization on Hopf surfaces
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• Supersymmetric counterterms from new minimal supergravity
• Massive N=2 Supergravity in Three Dimensions
• From multi-gravitons to Black holes: The role of complex saddles
• Consistency of supersymmetric 't Hooft anomalies
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• The Yang-Mills duals of small AdS black holes

Cited by in corpus (32)

• A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index
• Corrections to AdS${}_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity
• Higher-Derivative Corrections and AdS${}_5$ Black Holes
• AdS${}_5$ Holography and Higher-Derivative Supergravity
• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
• Exact Stringy Microstates from Gauge Theories
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Large $N$ Superconformal Indices for 3d Holographic SCFTs
• Supersymmetric phases of AdS${}_4$/CFT${}_3$
• Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions
• Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS${}_5$
• Boundary terms and conserved charges in higher-derivative gauged supergravity
• Schur Indices of Class $\mathcal{S}$ and Quasimodular Forms
• The Surprising Effectiveness of Weyl Gravity in Probing Quantum Corrections to AdS Black Holes
• Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM
• Supersymmetric Grey Galaxies, Dual Dressed Black Holes and the Superconformal Index
• Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae
• The large-$N$ limit of 4d superconformal indices for general BPS charges
• Root of unity asymptotics for Schur indices of 4d Lagrangian theories
• How to Build a Black Hole out of Instantons
• S-duality in the Cardy-like limit of the superconformal index
• A Family of Vertex Algebras from Argyres-Douglas Theory
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Wrapped M5-branes and AdS${}_5$ Black Holes
• Hawking-Page transition on a spin chain
• Supersymmetric zeta functions and determinants
• Universal Cardy-Like Behavior of 3D Partition Functions from Supersymmetric Localization
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS${}_4$ Black Holes
• Off-shell phase diagram of BPS black holes in AdS${}_5$