Correlator correspondences for subregular W-algebras and principal W-superalgebras

We examine a strong/weak duality between a Heisenberg coset of a theory with sl n subregular W-algebra symmetry and a theory with a 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 Rapcak 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 W-superalgebra appears as its symmetry and the properties of the superalgebra are less understood than bosonic counterparts.

Automated summary

In this study, a strong/weak duality between a Heisenberg coset with sl n subregular W-algebra symmetry and a theory with sl(n|1)-structure is examined. Correlator correspondences for a series of generalized duality are derived, as part of a project to realize duality of corner vertex operator algebras proposed by Gaiotto and Rapcak. Another type of duality involving an additional pair of fermions is also examined, which is a natural generalization of the fermionic FZZ-duality.