Phases of a strongly coupled four-fermion theory

Abstract

We present ongoing investigations of a four-dimensional lattice field theory with four massless reduced staggered fermions coupled through an SU(4)-invariant fourfermion interaction. As in previous studies of four-fermion and Higgs-Yukawa models with different lattice fermion discretizations, we observe a strong-coupling phase in which the system develops a mass gap without breaking any lattice symmetry. This symmetric strong-coupling phase is separated from the symmetric weak-coupling phase by a narrow region of four-fermi coupling in which the system exhibits long-range correlations.Speaker,

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.…”

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

“…The motivation for this work comes from recent numerical studies [1][2][3][4][5][6][7][8] of a particular lattice four fermion theory constructed using reduced staggered fermions [9]. In three dimensions this theory appears to exist in two phases -a free massless phase and a phase in which the fermions acquire a mass [1][2][3][4].…”

Exotic Phases of a Higgs-Yukawa Model withReduced Staggered Fermions

“…[2,3]. While a single peak is observed in a certain fermion susceptibility the eventual consensus of this earlier work was that this peak straddled a very narrow symmetry broken phase bordered by two phase transitions [4]. In Ref.…”

“…with P + projecting the antisymmetric matrix field σ(x) to its self-dual component which transforms under only one of the SU(2) factors comprising SO (4). It is the presence of the additional SU(2) symmetry of the fermion operator that allows one to prove the associated Pfaffian operator is real, positive semi-definite and hence the model can be simulated without encountering a sign problem.…”