Abstract
We examine a strong/weak duality between a Heisenberg coset of a theory with mathfrak{sl} n subregular mathcal{W} -algebra symmetry and a theory with a mathfrak{sl} n|1-structure. In a previous work, two of the current authors provided a path integral derivation of correlator correspondences for a series of generalized Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality. In this paper, we derive correlator correspondences in a similar way but for a different series of generalized duality. This work is a part of the project to realize the duality of corner vertex operator algebras proposed by Gaiotto and Rapčák and partly proven by Linshaw and one of us in terms of two dimensional conformal field theory. We also examine another type of duality involving an additional pair of fermions, which is a natural generalization of the fermionic FZZ-duality. The generalization should be important since a principal mathcal{W} -superalgebra appears as its symmetry and the properties of the superalgebra are less understood than bosonic counterparts.
Highlights
In a recent paper [15], the range of applicability was significantly enlarged
We examine a strong/weak duality between a Heisenberg coset of a theory with sln subregular W-algebra symmetry and a theory with a sln|1-structure
The generalization should be important since a principal W-superalgebra appears as its symmetry and the properties of the superalgebra are less understood than bosonic counterparts
Summary
The general construction of W-superalgebras has been first rigorously introduced by Kac and Wakimoto [31]. Let k and be related by (k − n)( − n) = 1, the Wn-algebras at level k and are isomorphic This is the self-duality of principal W-algebras, the Feigin-Frenkel duality [35]. In the case of the Feigin-Semikhatov algebras, that is the subregular W-algebras of sln, the statement is as follows This Walgebra has a free boson as subalgebra and one can consider the coset, see [40, 41] for studies of cosets of rational theories. Let k and be related by (k − n)( − n) = 1, this coset of the subregular W-algebras of sln at level k is isomorphic to the free boson coset of the principal W-superalgebra of sln|1. Free field realizations are a good starting point and we can rederive this duality using our path integral formalism and get a full duality of conformal field theories in the sense that we get a precise matching of correlation functions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
