Symmetric Mass Generation with four SU(2) doublet fermions

We simulate $ SU(2) $ lattice gauge theory using dynamical reduced staggered fermions. The latter lead to two rather than four Dirac fermions in the continuum limit. We review the derivation and properties of reduced staggered fermions and show that in the case of fields in the fundamental representation of $SU(2)$ the theory does not exhibit a sign problem and can be simulated using the RHMC algorithm. We present results on lattices up to $16^4$ for a wide range of bare ferm...

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...

It is expected that SU(2) gauge theory with $N_f$ fundamental fermions has an infrared fixed point when $N_f$ is between $\sim 6$ and 10. We study the hadron spectrum and scale setting in SU(2) gauge field theory with $N_f=2,4,6$ using hypercubic stout smeared Wilson-clover (HEX) action. The case $N_f=2$ is QCD-like, whereas $N_f=6$ is close to the lower edge of the conformal window. In our study the length scales are determined by using the gradient flow approach.

We use Monte Carlo simulation to probe the phase structure of a SU(2) gauge theory containing $N_f$ Dirac fermion flavors transforming in the fundamental representation of the group and interacting through an additional four fermion term. Pairs of physical flavors are implemented using the two tastes present in a reduced staggered fermion formulation of the theory. The resultant lattice theory is invariant under a set of shift symmetries which correspond to a discrete subgrou...

The phase diagrams at high temperature of SU(N) gauge theories with massive fermions are calculated by numerically minimizing the one-loop effective potential. We consider fermions in the Fundamental (F), Adjoint (Adj), Antisymmetric (AS), and Symmetric (S) representations, for N from 3 to 9, with periodic and antiperiodic boundary conditions applied. For one flavour of AS/S (Dirac) fermion with periodic boundary conditions the C-breaking phase is favoured perturbatively for ...

Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous...

The bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry protected topological phase and the trivial phase. In this work, we derive a description of this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors ($N_f=4$). This allows us to describe the transition in a lattice model with the maximal microscopic symmetry: an internal SO(4) symmetry. Within a systematic renormalization group analysis, we iden...

We have measured the running coupling constant of SU(3) gauge theory coupled to Nf=2 flavors of symmetric representation fermions, using the Schrodinger functional scheme. Our lattice action is defined with hypercubic smeared links which, along with the larger lattice sizes, bring us closer to the continuum limit than in our previous study. We observe that the coupling runs more slowly than predicted by asymptotic freedom, but we are unable to observe fixed point behavior bef...

We apply Schrodinger-functional techniques to the SU(2) lattice gauge theory with N_f=2 flavors of fermions in the adjoint representation. Our use of hypercubic smearing enables us to work at stronger couplings than did previous studies, before encountering a critical point and a bulk phase boundary. Measurement of the running coupling constant gives evidence of an infrared fixed point g* where 1/g*^2 = 0.20(4)(3). At the fixed point, we find a mass anomalous dimension gamma_...

An equivariantly gauge-fixed non-abelian gauge theory is a theory in which a coset of the gauge group, not containing the maximal abelian subgroup, is gauge fixed. Such theories are non-perturbatively well-defined. In a finite volume, the equivariant BRST symmetry guarantees that expectation values of gauge-invariant operators are equal to their values in the unfixed theory. However, turning on a small breaking of this symmetry, and turning it off after the thermodynamic limi...