A Perturbative Approach to Symmetric Mass Generation

TL;DR

This paper introduces a perturbative method using epsilon-expansion to analyze symmetric mass generation transitions, revealing universal critical behavior in models where interactions induce a gap without breaking symmetry.

Contribution

It develops a controlled perturbative framework for studying symmetric mass generation transitions, providing insights into their universal critical properties.

Findings

Identified a single-parameter-tuned transition in models of SMG

Computed universal critical quantities for these transitions

Proposed a conjecture for the universal behavior of SMG transitions

Abstract

The Landau paradigm has been a powerful framework for understanding phase transitions involving spontaneous symmetry breaking. In contrast, phase transitions between two symmetric phases, where neither phase breaks any symmetry, remain less explored. One intriguing class of such transitions involves "symmetric mass generation" (SMG), where interactions drive a transition from a gapless symmetric phase to a gapped symmetric phase. In this work, we develop a controlled perturbative approach to study a class of such transitions, based on an $\epsilon$-expansion around the critical dimension where the SMG-inducing-interaction becomes marginal. Applying this method to two distinct models, we identify a single-parameter-tuned transition in each case, which we conjecture captures the universal critical behavior of the SMG transition in these models. We compute universal quantities associated with these transitions.