Comments on Symmetric Mass Generation in 2d and 4d

TL;DR

The paper investigates symmetric mass generation (SMG) as a mechanism to gap chiral fermions while preserving a non-anomalous symmetry $G$ in both $d=3+1$ and $d=1+1$ dimensions. In four dimensions it constructs explicit paths using an auxiliary anomaly-free group $H$ and strong dynamics—including the well-controlled phenomenon of $s$-confinement—to convert chiral representations into vector-like ones that can be gapped by $G$-preserving operators; both supersymmetric (e.g., $H=SO(N+4)$ SQCD) and putative non-supersymmetric routes (e.g., $H=SU(N+4)$) are discussed, with a weakly coupled color-flavor locked Higgs description illuminating the gapped phase. In two dimensions SMG is achieved via Abelian and non-Abelian gauge dynamics, leveraging exactly marginal current-current deformations on the Narain moduli space or conjectured IR confined phases that furnish gauge-invariant massless fermions which can be gapped by higher-dimension operators, while respecting continuous symmetry $G$. The results illuminate multiple concrete routes to symmetry-preserving mass gaps and reveal when weak coupling descriptions suffice versus when strongly coupled sectors (and potential lattice implications) are essential.

Abstract

Symmetric mass generation is the name given to a mechanism for gapping fermions while preserving a chiral, but necessarily non-anomalous, symmetry. In this paper we describe how symmetric mass generation for continuous symmetries can be achieved using gauge dynamics in two and four dimensions. Various strong coupling effects are invoked, including known properties of supersymmetric gauge theories, specifically the phenomenon of s-confinement, and conjectured properties of non-supersymmetric chiral gauge theories.