The ordered phase of charged N=4 SYM plasma

TL;DR

This paper identifies a new ordered conformal phase of strongly coupled N=4 SYM plasma with a U(1) R-charge, existing at high temperatures and characterized by a non-zero expectation value of a dimension-2 operator.

Contribution

The authors construct and analyze a novel homogeneous and isotropic phase of N=4 SYM plasma that dominates in the microcanonical ensemble, extending the understanding of phase structure at high temperatures.

Findings

The new phase exists at arbitrary high temperatures, T >> μ.

It is characterized by an expectation value of a dimension-2 operator proportional to T^2.

In the limit μ/T → 0, the phase has vanishing energy and entropy densities.

Abstract

Recently is has been shown \cite{Gladden:2024ssb} that strongly coupled ${\cal N}=4$ supersymmetric Yang-Mills plasma with diagonal $U(1)$ $R$-charge chemical potential is unstable at $\frac{\mu}{2\pi T}=\sqrt{2}$. We construct a new homogeneous and isotropic phase of this plasma that dominates in the microcanonical ensemble (but not in the grand canonical one). The new phase extends to arbitrary high temperatures, \ie as $T\gg \mu$, and is characterized by an expectation value of a dimension-2 operator, with ${\cal O}_2\propto T^2$ -- it is the {\it ordered conformal phase}. In the limit $\frac\mu T\to 0$, this ordered phase has vanishing energy density $\frac{{\cal E}}{T^4}\propto \frac{\mu^2}{T^2}$ and is a low entropy density state $\frac{{\cal S}}{T^3}\propto \frac{\mu^2}{T^2}$.