The M2/M5 BPS Partition Functions from Supergravity

TL;DR

This paper computes the supersymmetric partition functions of M2 and M5 brane theories via supergravity duals, revealing phase transitions, stability constraints, and connections to the Witten Index in the context of AdS/CFT.

Contribution

It provides the first supergravity-based calculation of BPS partition functions for M2 and M5 brane theories, uncovering phase structure and stability insights.

Findings

Identified phase transitions in BPS partition functions.

Discovered unstable BPS black hole configurations.

Linked BPS partition functions to the Witten Index.

Abstract

In the framework of the AdS/CFT duality, we calculate the supersymmetric partition function of the superconformal field theories living in the world volume of either $N$ $M2$-branes or $N$ $M5$-branes. We used the dual supergravity partition function in a saddle point approximation over supersymmetric Black Holes. Since our BHs are written in asymptotically global $AdS_{d+1}$ co-ordinates, the dual SCFTs are in $R x S^{d}$ for $d=2,5$. The resulting partition function shows phase transitions, constraints on the phase space and allowed us to identify unstable BPS Black hole in the $AdS$ phase. These configurations should correspond to unstable configurations in the dual theory. We also report an intriguing relation between the most general Witten Index, computed in the above theories, and our BPS partition functions.