Speaker
Description
Recently, lattice formulations of two-dimensional chiral gauge theories via bosonization have been developed. These formulations are based on boson–fermion duality in the continuum limit. In this talk, we present a lattice construction of the gauged Wess–Zumino–Witten (WZW) model for two-dimensional $SU(N)$ chiral gauge theories. The WZW model contains a three-dimensional bulk contribution that reflects the gauge anomaly of chiral fermions. We show that the bulk dependence associated with the gauge anomaly cancels exactly at finite lattice spacing when the left and right fermion representations have identical quadratic indices. This is the same anomaly-free condition as in the continuum theory. Under this condition, exact gauge invariance is realized on the lattice.