A gravity interpretation for the complex Euclidean saddles of the ABJM index

TL;DR

This paper explores the gravitational interpretation of complex saddle points in the ABJM index, linking superconformal index calculations to black hole entropy and brane instabilities in AdS spacetime.

Contribution

It introduces a gravity-based interpretation for the complex Euclidean saddles of the ABJM index, extending the understanding of black hole microstates and brane instabilities.

Findings

Identifies a gravity interpretation for complex saddles in the ABJM index.

Connects the index's shifted chemical potentials to M5-brane instability.

Provides insights into the entropy of black holes via superconformal index analysis.

Abstract

The superconformal index is a grand-canonical partition function that counts the 1/16-BPS states in the theory, and its Legendre transform with respect to reduced chemical potentials accounts for the Bekenstein-Hawking entropy of electrically charged rotating black holes in anti-de Sitter spacetime. However, the superconformal index of $\mathcal{N}=4$ super Yang-Mills theory appears to allow shifts in chemical potentials, and the contributions of the shifted terms diverge exponentially. This puzzle was resolved by showing the instability of wrapped D3-branes corresponding to the shifts in the gravitational on-shell action. Analogously, we study the ABJM index and the M5-brane instability criterion.