scholarly journals From the representation theory of vertex operator algebras to modular tensor categories in conformal field theory

2005 ◽  
Vol 102 (15) ◽  
pp. 5304-5305 ◽  
Author(s):  
J. Lepowsky
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Representation Theory ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Tensor Categories ◽  
Conformal Field ◽  
Modular Tensor Categories

scholarly journals Correlator correspondences for subregular $$ \mathcal{W} $$-algebras and principal $$ \mathcal{W} $$-superalgebras

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Thomas Creutzig ◽  
Yasuaki Hikida ◽  
Devon Stockal
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Path Integral ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Natural Generalization ◽  
Weak Duality ◽  
Two Dimensional ◽  
Conformal Field ◽  
Corner Vertex

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

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