RENORMALIZATION OF THE SINE-GORDON MODEL AND NONCONSERVATION OF THE KINK CURRENT

We renormalize the (1 + 1)-dimensional sine-Gordon model by placing it on a Euclidean lattice, and study the renormalization group flow. We start with a compactified theory with controllable vortex activity. In the continuum limit the theory has a phase in which the kink current is anomalous, with divergence given by the vortex density. The phase structure is quite complicated. Roughly speaking, the system is normal for small coupling T. At the Kosterlitz-Thouless pooint T = pi/2, the current can become anomalous. At the Coleman point T = 8-pi, either the current becomes anomalous or the theory becomes trivial.