M2-brane indices on Higgs vacua and black holes

TL;DR

This paper investigates the superconformal index of a 3d gauge theory dual to M-theory on AdS4, revealing quantum black hole microstates and phase structures through high-order computations and complex analysis.

Contribution

It provides the first detailed analysis of finite-$N$ superconformal indices for the 3d ADHM quiver, uncovering signatures of quantum black hole states and phase transitions.

Findings

Identification of quantum black hole microstates in the finite-$N$ spectrum.

Discovery of a complex-$eta$ phase diagram with multiple peaks.

Connection between the index's Hilbert series limit and black hole entropy.

Abstract

As an exact count of protected states, the superconformal index provides a powerful probe into holography and quantum aspects of gravity, reproducing the Bekenstein--Hawking entropy of supersymmetric AdS black holes in the large-$N$ limit. As a step toward understanding quantum black hole microstates, we study the finite-$N$ index of the 3d ADHM quiver gauge theory, a UV description of the 3d $\mathcal N=8$ SCFT dual to M-theory on AdS$_4 \times S^7$. In this note, we analyze both microcanonical and canonical features of the superconformal index. By computing the index to sufficiently high orders using the factorization formula, we identify signatures of quantum black hole states in the finite-$N$ spectrum of the ADHM quiver, which align with the leading large-$N$ contribution reflecting the holographic dual black hole entropy. Furthermore, we introduce the complex-$\beta$ phase diagram of the index, which exhibits distinct peaks potentially associated with different gravitational saddles. We also examine the Hilbert series limit of the factorized index. Our results demonstrate that the finite-$N$ index encodes rich information about black hole microstates and their quantum gravitational interpretation.