Truncated conformal space approach for perturbed Wess–Zumino–Witten [formula omitted] models

Abstract

We outline the application of the truncated conformal space approach (TCSA) to perturbations of SU(2)k Wess–Zumino–Witten theories. As examples of this methodology, we consider two distinct perturbations of SU(2)1 and one of SU(2)2. SU(2)1 is first perturbed by its spin-1/2 field, a model which is equivalent to the sine-Gordon model at a particular value of its coupling β. The sine-Gordon spectrum is correctly reproduced as well as the corresponding finite-size corrections. We next study SU(2)1 with a marginal current–current perturbation. The TCSA results can be matched to perturbation theory within an appropriate treatment of the UV divergences. We find however that these results do not match field theoretic computations on the same model performed with a Lorentz invariant regulator. Finally, we consider SU(2)2 perturbed by its spin-1 field, which is equivalent to three decoupled massive Majorana fermions. In this case as well the TCSA reproduces accurately the known spectrum.