Correlator correspondences for Gaiotto-Rapcak dualities and first order formulation of coset models

We derive correspondences of correlation functions among dual conformal field theories in two dimensions by developing a first order formulation of coset models. We examine several examples, and the most fundamental one may be a conjectural equivalence between a coset (SL(n)(k)circle times SL(n)(-1))/SL(n)(k-1) and sl(n) Toda field theory with generic level k. Among others, we also complete the derivation of higher rank FZZ-duality involving a coset SL(n +1)(k)/(SL(n)(k) circle times U(1)), which could be done only for n = 2, 3 in our previous paper. One obstacle in the previous work was our poor understanding of a first order formulation of coset models. In this paper, we establish such a formulation using the BRST formalism. With our better understanding, we successfully derive correlator correspondences of dual models including the examples mentioned above. The dualities may be regarded as conformal field theory realizations of some of the Gaiotto-Rapcak dualities of corner vertex operator algebras.

Automated summary

Correspondences of correlation functions among dual conformal field theories in two dimensions are derived by developing a first order formulation of coset models. The most fundamental example may be a conjectural equivalence between a coset (SL(n)(k)circle times SL(n)(-1))/SL(n)(k-1) and sl(n) Toda field theory with generic level k. The study also completes the derivation of higher rank FZZ-duality involving a coset SL(n +1)(k)/(SL(n)(k) circle times U(1)).