SO(4) invariant Higgs-Yukawa model with reduced staggered fermions

Abstract

We explore the phase structure of a four dimensional SO(4) invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field. The fermions belong to the fundamental representation of the symmetry group while the three scalar field components transform in the self-dual representation of SO(4). The model is a generalization of a four fermion system with the same symmetries that has received recent attention because of its unusual phase structure comprising massless and massive symmetric phases separated by a very narrow phase in which a small bilinear condensate breaking SO(4) symmetry is present. The generalization described in this paper simply consists of the addition of a scalar kinetic term. We find a region of the enlarged phase diagram which shows no sign of a fermion condensate or symmetry breaking but in which there is nevertheless evidence of a diverging correlation length. Our results in this region are consistent with the presence of a single continuous phase transition separating the massless and massive symmetric phases observed in the earlier work.

Symmetric Mass Generation in Lattice Gauge Theory

“…Indeed, in this form, one can see that the kinetic term of this model is precisely the same as that considered in previous work with SO(4) invariant staggered fermions [3].…”

“…In [3], we showed that it is possible to achieve symmetric mass generation in this model for large values of the Yukawa coupling and vanishing gauge coupling. In this paper, we show that a four-fermion condensate can also be obtained by using strong gauge interactions and small Yukawa coupling.…”

“…The model can be seen as a generalization of the SO(4) Higgs-Yukawa theory described in [3], which uses strong quartic interactions to gap lattice fermions. This fourdimensional model is built on earlier work directed at symmetric mass generation with staggered fermions in two, three, and four dimensions [4][5][6][7][8][9][10].…”

Lattice gauge theory for physics beyond the Standard Model

“…They exhibit hyperscaling with universal critical exponents at the IRFP, and these critical exponents are relevant for mass generation in BSM models [7]. Although still in early stages, non-perturbative lattice investigations of other possible mechanisms for fermion mass generation [11][12][13][14][15][16][17] are also important and interesting to pursue.…”

Exotic Phases of a Higgs-Yukawa Model withReduced Staggered Fermions

“…Results for this model appeared in Ref. [6]. 1 In addition to its manifest SO(4) symmetry, the action is also invariant under a shift symmetry…”