Excited states in some simple perturbed conformal field theories

The method of analytic continuation is used to find exact integral equations for a selection of finite-volume energy levels for the non-unitary minimal models $M_{2,2N+3}$ perturbed by their $\varphi_{13}$ operators. The N=2 case is studied in particular detail. Along the way, we find a number of general results which should be relevant to the study of excited states in other models.