Comments on Symmetric Mass Generation in 2d and 4d

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.

Gauge Enhanced Quantum Criticality Beyond the Standard Model

“…Even if it condenses, it is not expected to gap out the Weyl fermions if its vaccum expectation value is small (but it will Higgs down the gauge group), so the theory remains gapless in the fermion sector in all phases. However, sufficiently strong Higgs condensation of TrΦ bi (or Φ 1 equivalently) can lead to symmetric mass generation (SMG) [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] as discussed previously.…”

“…The Symmetric Mass Generation (SMG) mechanism is explored in various references, for some selective examples, by Fidkowski-Kitaev[35] in 0+1d, by Wang-Wen[36,37] for gapping chiral fermions in 1+1d, You-He-Xu-Vishwanath[38,39] in 2+1d, and notable examples in 3+1d by Eichten-Preskill[40], Wen[41], You-BenTov-Xu[42,43], BenTov-Zee[44], Kikukawa[45], Catterall et al[46,47], Razamat-Tong[48,49], etc.12 Here fermions are anti-commuting Grassman variables, so this expression ψψψψ is only schematic. The precise expression of ψψψψ includes additional spacetime-internal representation indices and also includes possible additional spacetime derivatives (for point-splitting the fermions to neighbor sites if writing them on a regularized lattice).…”

Emergent strongly coupled ultraviolet fixed point in four dimensions with 8 Kähler-Dirac fermions

“…Most of the existing studies with 2 staggered fields found a first order bulk transition, and many identified a novel strong coupling phase that exhibits spontaneous breaking of the single-site shift symmetry of staggered fermions (S4 phase) [28]. The S4 phase appears to be chirally symmetric and confining 1 , conceivably describing symmetric mass generation (SMG) [29][30][31]. Two staggered fermion species in the massless limit are equivalent to four reduced staggered fields that correspond to 16 Weyl spinors.…”

Symmetric Mass Generation

“…In this case, although there is no obstruction towards gapping the fermions symmetrically, the mechanism to achieve the symmetric gapped state must go beyond the free-fermion (perturbatively free or weak-coupling) approach, which potentially leads to a non-perturbative strong-coupling approach in order to generate a finite excitation gap in the fermion many-body spectrum by non-trivial interaction effects. The strong-coupling [34] here refers to the coupling in the continuum field theory being nonperturbative, or the interaction energy being of the same order as the kinetic energy on the lattice scale (which may also be called the intermediate-strength interaction on a lattice). This phenomenon of gapping out massless fermions by interactions in an anomaly-free system without breaking the anomaly-free symmetry is now called the symmetric mass generation (SMG) [34,35].…”

“…The strong-coupling [34] here refers to the coupling in the continuum field theory being nonperturbative, or the interaction energy being of the same order as the kinetic energy on the lattice scale (which may also be called the intermediate-strength interaction on a lattice). This phenomenon of gapping out massless fermions by interactions in an anomaly-free system without breaking the anomaly-free symmetry is now called the symmetric mass generation (SMG) [34,35].…”