Thermodynamics of spinning D3-branes

TL;DR

This paper studies the thermodynamics of spinning D3-branes in supergravity, comparing supergravity results with a free super-Yang-Mills model, and proposes a mean field theory correction to match critical behavior.

Contribution

It introduces a naive free field model for spinning D3-branes and suggests a mean field correction to accurately reproduce critical exponents near stability limits.

Findings

Supergravity predicts a thermodynamic stability limit for spinning D3-branes.

Naive free super-Yang-Mills model approximates supergravity free energy within stability region.

Mean field theory correction improves critical exponent predictions.

Abstract

Spinning black three-branes in type IIB supergravity are thermodynamically stable up to a critical value of the angular momentum density. Inside the region of thermodynamic stability, the free energy from supergravity is roughly reproduced by a naive model based on free N=4 super-Yang-Mills theory on the world-volume. The field theory model correctly predicts a limit on angular momentum density, but near this limit it does not reproduce the critical exponents one can compute from supergravity. Analogies with Bose condensation and modified matrix models are discussed, and a mean field theory improvement of the naive model is suggested which corrects the critical exponents.