Thermal order in large N conformal gauge theories

TL;DR

This paper investigates spontaneous global symmetry breaking at all nonzero temperatures in certain large N conformal gauge theories, revealing persistent Higgs phases and symmetry-breaking phenomena linked to specific fixed points in coupling space.

Contribution

It demonstrates the existence of temperature-independent symmetry-breaking and Higgs phases in non-supersymmetric large N gauge theories with specific gauge groups, extending previous fractional dimension results.

Findings

Symmetry-breaking occurs at all nonzero temperatures in certain large N gauge theories.

Theories exhibit circles of fixed points with stable symmetry-breaking phases.

Global symmetries broken include a5_2 and U(1), with order parameters from bifundamental scalars.

Abstract

In this work we explore the possibility of spontaneous breaking of global symmetries at all nonzero temperatures for conformal field theories (CFTs) in $D = 4$ space-time dimensions. We show that such a symmetry-breaking indeed occurs in certain families of non-supersymmetric large $N$ gauge theories at a planar limit. We also show that this phenomenon is accompanied by the system remaining in a persistent Brout-Englert-Higgs (BEH) phase at any temperature. These analyses are motivated by the work done in arXiv:2005.03676 where symmetry-breaking was observed in all thermal states for certain CFTs in fractional dimensions. In our case, the theories demonstrating the above features have gauge groups which are specific products of $SO(N)$ in one family and $SU(N)$ in the other. Working in a perturbative regime at the $N\rightarrow\infty$ limit, we show that the beta functions in these theories yield circles of fixed points in the space of couplings. We explicitly check this structure up to two loops and then present a proof of its survival under all loop corrections. We show that under certain conditions, an interval on this circle of fixed points demonstrates both the spontaneous breaking of a global symmetry as well as a persistent BEH phase at all nonzero temperatures. The broken global symmetry is $\mathbb{Z}_2$ in one family of theories and $U(1)$ in the other. The corresponding order parameters are expectation values of the determinants of bifundamental scalar fields in these theories. We characterize these symmetries as baryon-like symmetries in the respective models.