EFT and the SUSY Index on the 2nd Sheet

TL;DR

This paper develops a 3d EFT approach to analyze the high-temperature behavior of the SUSY index on the second sheet, revealing insights into black hole microstates and phases in AdS$_5$ with robust confinement mechanisms.

Contribution

It introduces a novel 3d EFT framework to study the SUSY index's high-temperature limit on the second sheet, including conjectures about higher-order behavior and zero mode effects.

Findings

Derived the index behavior at orders β^{-2}, β^{-1}, and β^{0}

Conjectured the expansion truncates at O(β) with exponentially small corrections

Identified a non-perturbative confinement mechanism ensuring robustness

Abstract

The counting of BPS states in four-dimensional ${\cal N}=1$ 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.