Abstract
We describe a proposal for constructing a lattice theory that we argue may be capable of yielding free Weyl fermions in the continuum limit. The model employs reduced staggered fermions and uses site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. The possibility for such symmetric mass generation is tied to the cancellation of certain discrete anomalies arising in the continuum limit. The latter place strong constraints on the number of lattice fermions -- constraints that are satisfied by this model. We present numerical results for the model in two dimensions which support this sc
Highlights
It has long been a goal of lattice field theory to be able to describe continuum chiral gauge theories
In this paper we have described a new lattice fermion mirror model which employs reduced staggered fermions transforming in the real eight dimensional chiral representation of a Spin(7) symmetry group
Interactions are introduced via Yukawa interactions of Fidkowski-Kitaev type on even parity lattice sites which we argue are capable of generating mass for half of the lattice fermions without producing symmetry breaking bilinear fermion condensates
Summary
It has long been a goal of lattice field theory to be able to describe continuum chiral gauge theories. The early numerical work to test this idea made use of Wilson and staggered lattice fermions [4,5,6,7,8] and appeared to invalidate the approach—to generate large mirror masses required large four fermion or Yukawa couplings and typically this resulted in the formation of symmetry breaking condensates coupling left and right-handed states via Dirac mass terms [9] More recently this approach was revived for lattice fermion actions with superior chiral properties—in a series of papers Poppitz et al have investigated models using overlap fermions [10,11,12] while a gauge invariant path integral measure for overlap chiral fermions in SOð10Þ was constructed in [13]. We summarize our conclusions and discuss open questions in the final section of the paper
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