Thermodynamics of spinning D3-branes

TL;DR

This work analyzes the thermodynamics of spinning D3-branes by comparing type IIB supergravity results with a naive ${\cal N}=4$ SYM field theory model at finite temperature and R-charge. It identifies a boundary of thermodynamic stability controlled by the dimensionless ratio $j/(N^2T^3)$ and shows the gravity description yields a critical exponent $\gamma=1/2$ at the boundary. A regulation scheme for the free-field model is developed to obtain finite, peer-consistent predictions for the boundary location, though the naive model misses the correct exponent; a mean-field treatment of interactions is argued to reproduce $\gamma=1/2$ for a special permeability $\mu_0=2/3$, indicating the essential role of interactions in the critical behavior. The study highlights analogies with Bose condensation and Higgsing, and suggests a phase boundary beyond which a distinct stable phase (brane separation) may emerge.

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.

Figures (1)

• Figure 1: $c_\Omega$ as a function of $\Omega$ for fixed $T$, in supergravity (solid line) and in the naive field theory model (dashed line). The horizontal and vertical axes have been scaled differently for the two curves so that the boundary of stability occurs at the same point $\Omega_c$, and so that the two curves meet at $\Omega = 0$.