5d Black holes, wrapped fivebranes and 3d Chern-Simons Super Yang-Mills

TL;DR

This paper explores black hole solutions in 5d supergravity related to NS5-branes wrapping three-spheres, revealing thermodynamic instability above a critical temperature and presenting analytical solutions with specific temperature properties.

Contribution

It provides new extremal and non-extremal solutions in 5d supergravity describing wrapped NS5-branes and analyzes their thermodynamic behavior.

Findings

Black hole solutions have temperatures above the Hagedorn temperature.

Entropy decreases with increasing temperature, indicating instability.

An analytical solution with a linear dilaton has a temperature twice the critical temperature.

Abstract

We study extremal and non-extremal generalizations of the regular non-abelian solution found by Chamseddine and Volkov in 5d N=4 gauged supergravity, which has been shown by Maldacena and Nastase to describe a system of NS5-branes wrapping an three-sphere dual to three-dimensional U(N) N=1 supersymmetric Yang-Mills with Chern-Simons coupling k=N/2. All black hole solutions have a temperature larger than the Hagedorn temperature Tc of the little string theory and their entropy decreases as the temperature increases. This is a sign that the system is thermodynamically unstable above Tc. We have also found an analytical solution describing NS5-branes wrapped on a constant radius three-sphere and involving a linear dilaton. Its non-extremal generalization has a temperature equal to 2 Tc.