Chen Chen, Joel Giedt, Erich Poppitz
An approach to the formulation of chiral gauge theories on the lattice is to start with a vector-like theory, but decouple one chirality (the "mirror" fermions) using strong Yukawa interactions with a chirally coupled "Higgs" field. While this is an attractive idea, its viability needs to be tested with nonperturbative studies. The model that we study here, the so-called "3-4-5" model, is anomaly free and the presence of massless states in the mirror sector is not required by anomaly matching arguments, in contrast to the "1-0" model that was studied previously. We have computed the polarization tensor in this theory and find a directional discontinuity that appears to shrink to zero in the limit of an infinite lattice, which is equivalent to the continuum limit at fixed physical volume. We show that a similar behavior occurs for the free massive Ginsparg-Wilson fermion, where it is known that the polarization tensor is analytic in the continuum limit. We thus find tentative support for the conclusion that in the continuum limit of the 3-4-5 model, the mirror modes decouple, leaving behind a chiral gauge theory in the light sector. We end by discussing future work that can be useful to corroborate this conclusion
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http://arxiv.org/abs/1211.6947
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