Quantum vortices, M2-branes and black holes

TL;DR

This paper investigates the partition functions of BPS vortices and monopoles in M2-brane gauge theories, revealing how monopole condensation explains black hole entropy and suggesting finite N effects in the large N limit.

Contribution

It introduces two methods to analyze the Cardy limit of the index on S^2×R, connecting vortex and monopole contributions to black hole entropy in AdS4/CFT3.

Findings

Monopole condensation confines most degrees of freedom.

Large N free energy matches Bekenstein-Hawking entropy.

Finite N effects imply a residual N^{3/2} degrees of freedom.

Abstract

We study the partition functions of BPS vortices and magnetic monopole operators, in gauge theories describing $N$ M2-branes. In particular, we explore two closely related methods to study the Cardy limit of the index on $S^2\times\mathbb{R}$. The first method uses the factorization of this index to vortex partition functions, while the second one uses a continuum approximation for the monopole charge sums. Monopole condensation confines most of the $N^2$ degrees of freedom except $N^{\frac{3}{2}}$ of them, even in the high temperature deconfined phase. The resulting large $N$ free energy statistically accounts for the Bekenstein-Hawking entropy of large BPS black holes in $AdS_4\times S^7$. Our Cardy free energy also suggests a finite $N$ version of the $N^{\frac{3}{2}}$ degrees of freedom.