Symmetric Mass Generation

TL;DR

Symmetric Mass Generation (SMG) is a novel mechanism allowing fermions to acquire mass without symmetry breaking, with deep theoretical and practical implications, including connections to topological states and lattice gauge theories.

Contribution

This paper defines SMG, reviews numerical results, and introduces a new unifying theoretical framework encompassing various mechanisms and constructions.

Findings

SMG enables fermion mass without symmetry breaking.

SMG is connected to topological insulators and anomaly cancellations.

A new theoretical framework unifies different SMG mechanisms.

Abstract

The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechanism is generally referred to as the "Symmetric Mass Generation (SMG)." It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes current numerical results, introduces a novel unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and overviews various features and applications of SMG.