Finite Density States in Integrable Conformal Field Theories

We study states of large charge density in integrable conformal coset models. For the O(2) coset, we consider two different S-matrices, one corresponding to a Thirring mass perturbation and the other to the continuation to O(2+epsilon). The former leads to simplification in the conformal limit; the latter gives a more complicated description of the O(2) system, with a large zero mode sector in addition to the right- and left-movers. We argue that for the conformal O(2+2M|2M) supergroup coset, the S-matrix is given by the analog of the O(2+epsilon) construction.