Trialities of orthosymplectic W-algebras

Creutzig T, Linshaw AR (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Advances in Mathematics Elsevier

Book Volume: 409

Article Number: 108678

DOI: 10.1016/j.aim.2022.108678

Abstract

Trialities of W-algebras are isomorphisms between the affine cosets of three different W-(super)algebras, and were first conjectured in the physics literature by Gaiotto and Rapčák. In this paper we prove trialities among eight families of W-(super)algebras of types B, C, and D. The key idea is to identify the affine cosets of these algebras with one-parameter quotients of the universal two-parameter even spin W∞-algebra which was recently constructed by Kanade and the second author. Our result is a vast generalization of both Feigin-Frenkel duality in types B, C, and D, and the coset realization of principal W-algebras of type D due to Arakawa and us. It also provides a new coset realization of principal W-algebras of types B and C. As an application, we prove the rationality of the affine vertex superalgebra Lk(osp1|2n), the minimal W-algebra Wk−1/2(sp2n+2,fmin), and the coset Com(Lk(sp2m),Lk(sp2n)), for all integers k,n,m≥1 with m1|2n and osp2|2n, and subregular W-algebras of so2n+1.

Involved external institutions

University of Alberta CA Canada (CA) University of Denver US United States (USA) (US)

How to cite

APA:

Creutzig, T., & Linshaw, A.R. (2022). Trialities of orthosymplectic W-algebras. Advances in Mathematics, 409. https://doi.org/10.1016/j.aim.2022.108678

MLA:

Creutzig, Thomas, and Andrew R. Linshaw. "Trialities of orthosymplectic W-algebras." Advances in Mathematics 409 (2022).

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