Critical Behavior in the Rotating D-branes

TL;DR

This paper investigates phase transitions and critical behavior in rotating D-branes and related supergravity solutions, revealing ensemble-dependent shifts in critical points and the absence of Hawking-Page transitions in certain cases.

Contribution

It provides a detailed analysis of thermodynamic stability, critical exponents, and phase transitions in rotating D-branes and M-branes, including ensemble effects and scaling laws.

Findings

Critical behavior observed in rotating D3-, M5-, and M2-branes.

Critical exponents obey static scaling laws.

Hawking-Page transition depends on the ensemble and brane type.

Abstract

The low energy excitation of the rotating D3-branes is thermodynamically stable up to a critical angular momentum density. This indicates that there is a corresponding phase transition of the ${\cal N}$=4 large $N$ super Yang-Mills theory at finite temperature. On the side of supergravity, we investigate the phase transition in the grand canonical ensemble and canonical ensemble. Some critical exponents of thermodynamic quantities are calculated. They obey the static scaling laws. Using the scaling laws related to the correlation length, we get the critical exponents of the correlation function of gauge field. The thermodynamic stability of low energy excitations of the rotating M5-branes and rotating M2-branes is also studied and similar critical behavior is observed. We find that the critical point is shifted in the different ensembles and there is no critical point in the canonical ensemble for the rotating M2-branes. We also discuss the Hawking-Page transition for these rotating branes. In the grand canonical ensemble, the Hawking-Page transition does not occur. In the canonical ensemble, however, the Hawking-Page transition may appear for the rotating D3- and M5-branes, but not for the rotating M2-branes.