Symmetric Mass Generation

Massless 2+1D Dirac fermions arise in a variety of systems from graphene to the surfaces of topological insulators, where generating a mass is typically associated with breaking a symmetry. However, with strong interactions, a symmetric gapped phase can arise for multiples of eight Dirac fermions. A continuous quantum phase transition from the massless Dirac phase to this massive phase, which we term Symmetric Mass Generation (SMG), is necessarily beyond the Landau paradigm a...

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...

Using lattice simulations we demonstrate from first principles the existence of a non-perturbative mechanism for elementary particle mass generation in models with gauge fields, fermions and scalars, if an exact invariance forbids power divergent fermion masses and fermionic chiral symmetries broken at UV scale are maximally restored. We show that in the Nambu-Goldstone phase a fermion mass term, unrelated to the Yukawa operator, is dynamically generated. In models with elect...

We study a single exactly massless staggered fermion in the fundamental representation of an $SU(2)$ gauge group. We utilize an nHYP-smeared fermion action supplemented with additional heavy Pauli-Villars fields which serve to decrease lattice artifacts. The phase diagram exhibits a clear two-phase structure with a conformal phase at weak coupling and a novel new phase, the Symmetric Mass Generation (SMG) phase, appearing at strong coupling. The SMG phase is confining with al...

We investigate a proposal to address several outstanding shortcomings of the perturbative Standard Model (SM) of particle physics. The appeal of this proposal is that these features are a manifestation of the non-perturbative sector of the SM, requiring no assumptions about new physics beyond presently attainable experimental limits. In this thesis we apply non-perturbative techniques to two complementary models: a toy 4-fermion model containing explicit chiral symmetry-break...

The K\"ahler-Dirac fermion, recognized as an elegant geometric approach, offers an alternative to traditional representations of relativistic fermions. Recent studies have demonstrated that symmetric mass generation (SMG) can precisely occur with two copies of K\"ahler-Dirac fermions across any spacetime dimensions. This conclusion stems from the study of anomaly cancellation within the fermion system. Our research provides an alternative understanding of this phenomenon from...

Using a simple three dimensional lattice four-fermion model we argue that massless fermions can become massive due to interactions without the need for any spontaneous symmetry breaking. Using large scale Monte Carlo calculations within our model, we show that this non-traditional mass generation mechanism occurs at a second order quantum critical point that separates phases with the same symmetries. Universality then suggests that the new origin for the fermion mass should b...

In this talk we present a numerical lattice study of an SU(3) gauge model where an SU(2) doublet of non-Abelian strongly interacting fermions is coupled to a complex scalar field doublet via a Yukawa and a Wilson-like term. The model enjoys an exact symmetry, acting on all fields, which prevents UV power divergent fermion mass corrections, despite the presence of these two chiral breaking operators in the Lagrangian. In the phase where the scalar potential is non-degenerate a...

The strongly coupled lattice gauge models with confined fermion and scalar matter fields, which in a certain phase break dynamically a global chiral symmetry, are reconsidered from the point of view of the existence of heavy fermions. If these models are interpreted as describing a new strong force beyond the standard model, such heavy fermions can arise as neutral bound states of the fundamental fermion and scalar. The discussed mechanism could be considered as an alternativ...

We propose a novel solution to the Strong CP problem -- to explain why SU(3) strong force has a nearly zero theta angle $\bar\theta_3 \simeq 0$ for the 4d Standard Model (SM). The new ingredient is Symmetric Mass Generation (SMG): symmetry-preserving mass or energy gap can be generated without breaking any symmetry $G$ and without any quadratic mean-field mass deformation as long as $G$ is all perturbative local and nonperturbative global anomaly-free. In our first model, we ...