Higher rank FZZ-dualities

Abstract

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 $$ \mathfrak{sl}(2)/\mathfrak{u}(1) $$ 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 $$ \mathfrak{sl}(2) $$ 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 $$ \mathfrak{sl}\left(N+1\right)/\left(\mathfrak{sl}(N)\times \mathfrak{u}(1)\right) $$ and investigate the equivalence to a theory with an sl N + 1 N $$ \mathfrak{sl}\left(N+\left.1\right|N\right) $$ structure. We derive the duality explicitly for N = 2, 3 by applying recent works on the reduction method extended for sl N $$ \mathfrak{sl}(N) $$ 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 Y 0,N,N+1[ψ] and Y N,0,N+1[ψ −1].

Keywords

• Conformal and W Symmetry
• Conformal Field Theory
• String Duality