IAS Physics Group Meeting

Abstract: Can we regularize chiral global symmetries and their anomalies on a lattice with a finite dimensional Hilbert space? We discuss how the vector and axial U(1) symmetries of a massless Dirac fermion in 1+1d are realized in the conventional staggered fermion lattice model. Interestingly, these two lattice charges do not commute and form an infinite dimensional algebra. We prove that these symmetries force the low-energy phase to be gapless, reminiscent of consequences from perturbative anomalies of continuous global symmetries in quantum field theory.