Higher rank FZZ-dualities

Abstract

We examine strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten’s cigar model described by the sl(2)/u(1) coset and sine-Liouville theory. In a previous work, a proof of the FZZ-duality was provided by applying the reduction method from sl(2) Wess-Zumino-Novikov-Witten model to Liouville field theory and the self-duality of Liouville field theory. In this paper, we work with the coset model of the type sl(N+1)/(sl(N)×u(1)) and investigate the equivalence to a theory with an sl(N+1|N) structure. We derive the duality explicitly for N = 2, 3 by applying recent works on the reduction method extended for sl(N) and the self-duality of Toda field theory. Our results can be regarded as a conformal field theoretic derivation of the duality of the Gaiotto-Rapčák corner vertex operator algebras Y0, N, N+1[ψ] and YN, 0, N+1[ψ⁻¹].