Chiral Lattice Gauge Theories and the Strong Coupling Dynamics of a Yukawa-Higgs Model with Ginsparg-Wilson Fermions

The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge theories described in hep-lat/0605003 uses exact lattice chirality to decouple the massless chiral fermions from a mirror sector, whose strong dynamics is conjectured to give cutoff-scale mass to the mirror fermions without breaking the chiral gauge symmetry. In this talk, we report on our study of the mirror sector dynamics of a two-dimensional chiral gauge theory in the limit of strong Yukawa and vanishing gauge couplings, in which case it reduces to an $XY$ model coupled to Ginsparg-Wilson fermions. For the mirror fermions to acquire cutoff-scale mass it is believed to be important that the $XY$ model remain in its ``high temperature'' phase, where there is no algebraic ordering---a conjecture supported by the results of our work. We use analytic and Monte-Carlo methods with dynamical fermions to study the scalar and fermion susceptibilities, and the mirror fermion spectrum. Our results provide convincing evidence that the strong dynamics does not ``break" the chiral symmetry (more precisely, that the mirror fermions do not induce algebraic ordering in two-dimensions), and that the mirror fermions decouple from the infrared physics.