The free and safe fate of symmetry non-restoration

TL;DR

This paper explores the high-temperature behavior of four-dimensional gauge-Yukawa theories, revealing a class of asymptotically free theories where symmetry remains broken even at arbitrarily high temperatures.

Contribution

It identifies a new class of complete asymptotically free theories that exhibit symmetry breaking at all temperatures, including the high-temperature limit.

Findings

Discovered theories with symmetry breaking persisting at high temperatures.

Provided examples of asymptotically safe theories with non-restoring symmetry.

Expanded understanding of phase behavior in gauge-Yukawa theories.

Abstract

We investigate the high temperature fate of four dimensional gauge-Yukawa theories featuring short distance conformality of either interacting or non-interacting nature. The latter is known as complete asymptotic freedom and, as templates, we consider non-abelian gauge theories featuring either two singlet scalars coupled to gauged fermions via Yukawa interactions or two gauged scalars with(out) fermions. For theories with interacting fixed points at short distance, known as asymptotically safe, we consider two calculable examples. Exploring the landscape of safe and free theories above we discover a class of complete asymptotically free theories for which symmetry breaks at arbitrary high temperatures. In its minimal form this class is constituted by a theory with two fundamental gauged scalars each gauged under an independent group.