FZZ-triality and large N=4 super Liouville theory

Abstract

We examine dualities of two dimensional conformal field theories by applying the methods developed in previous works. We first derive the duality between SL(2|1)k/(SL(2)k⊗U(1)) coset and Witten's cigar model or sine-Liouville theory. The latter two models are Fateev-Zamolodchikov-Zamolodchikov (FZZ-)dual to each other, hence the relation of the three models is named FZZ-triality. These results are used to study correlator correspondences between large N=4 super Liouville theory and a coset of the form Y(k1,k2)/SL(2)k1+k2, where Y(k1,k2) consists of two SL(2|1)ki and free bosons or equivalently two U(1) cosets of D(2,1;ki−1) at level one. These correspondences are a main result of this paper. The FZZ-triality acts as a seed of the correspondence, which in particular implies a hidden SL(2)k′ in SL(2|1)k or D(2,1;k−1)1. The relation of levels is k′−1=1/(k−1). We also construct boundary actions in sine-Liouville theory as another use of the FZZ-triality. Furthermore, we generalize the FZZ-triality to the case with SL(n|1)k/(SL(n)k⊗U(1)) for arbitrary n>2.