Feigin-Semikhatov conjecture and related topics

Abstract

Feigin-Semikhatov conjecture, now established, states algebraic isomorphisms between the cosets of the subregular $\mathcal{W}$-algebras and the principal $\mathcal{W}$-superalgebras of type A by their full Heisenberg subalgebras. It can be seen as a variant of Feigin-Frenkel duality between the ${\mathcal{W}}_n$-algebras and also as a generalization of the connection between the $\mathcal{N}=2$ superconformal algebra and the affine algebra ${\widehat{\mathfrak{sl}}}_{2,k}$.We review the recent developments on the correspondence of the subregular W-algebras and the principal W-superalgebras of type A at the level of algebras, modules and intertwining operators, including fusion rules.

This is a review paper for Int. J. Mod. Phys. A. 25 pages. Comments welcome

References in corpus (3)

• Trialities of orthosymplectic $\mathcal{W}$-algebras
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• Subregular W-algebras of type A