FZZ-triality and large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">N</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">=</mml:mo><mml:mn>4</mml:mn></mml:math> super Liouville theory

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