Abstract
We construct a four-dimensional lattice gauge theory in which fermions acquire mass without breaking symmetries as a result of gauge interactions. Our model consists of reduced staggered fermions transforming in the bifundamental representation of an SU(2)×SU(2) gauge symmetry. This fermion representation ensures that single-site bilinear mass terms vanish identically. A symmetric four-fermion operator is however allowed, and we give numerical results that show that a condensate of this operator develops in the vacuum.
Highlights
Can we generate a mass for all physical states in a theory without breaking symmetries? Can we do this using gauge interactions only? In this paper, we describe a lattice model that is capable of realizing this scenario
A symmetric four-fermion operator remains invariant under these symmetries, and we present evidence that it condenses as a result of the gauge interactions
We argued that a particular lattice gauge theory composed of massless reduced staggered fermions transforming under a local SU (2) × SU (2) symmetry develops a four-fermion rather than bilinear-fermion condensate due to confinement
Summary
Since no symmetries are broken by this condensate, there are no massless Goldstone bosons, and the spectrum consists of color singlet composites of the elementary fermions This scenario corresponds to symmetric mass generation realized in the context of a confining gauge theory. 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]. Both of the SU (2) subgroups of SO(4) are gauged, and confinement rather than strong Yukawa interactions is used to generate the four-fermion condensate
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