The continuum limit of aN−1(2) spin chains

Building on our previous work for a2(2) and a3(2) we explore systematically the continuum limit of gapless aN−1(2) vertex models and spin chains. We find the existence of three possible regimes. Regimes I and II for a2n−1(2) are related with a2n−1(2) Toda, and described by n compact bosons. Regime I for a2n(2) is related with a2n(2) Toda and involves n compact bosons, while regime II is related instead with B(1)(0,n) super Toda, and involves in addition a single Majorana fermion. The most interesting is regime III, where non-compact degrees of freedom appear, generalising the emergence of the Euclidean black hole CFT in the a2(2) case. For a2n(2) we find a continuum limit made of n compact and n non-compact bosons, while for a2n−1(2) we find n compact and n−1 non-compact bosons. We also find deep relations between aN−1(2) in regime III and the gauged WZW models SO(N)/SO(N−1).