A bstract We revisit the symmetries of massless two-dimensional adjoint QCD with gauge
group SU (N). The dynamics is not sufficiently constrained by the ordinary symmetries and …

We prove the long-standing conjecture on the coset construction of the minimal series
principal W-algebras of ADE types in full generality. We do this by first establishing Feigin's …

We prove the conjecture of Gaiotto and Rap\v {c}\'ak that the $ Y $-algebras $ Y_ {L, M,
N}[\psi] $ with one of the parameters $ L, M, N $ zero, are simple one-parameter quotients of …

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 …

A bstract We initiate the study of how the insertion of magnetically charged states in 4d self-
dual gauge theories impacts the 2d chiral algebras supported on the celestial sphere at …

Let V be a simple vertex operator algebra containing a rank n Heisenberg vertex algebra H
and let C= Com (H; V) be the coset of H in V. Assuming that the module categories of interest …

We define new deformable families of vertex operator algebras A g, Ψ, σ A g, Ψ, σ
associated to a large set of S-duality operations in four-dimensional supersymmetric gauge …

We construct two non-semisimple braided ribbon tensor categories of modules for each
singlet vertex operator algebra M (p), p≥ 2. The first category consists of all finite-length M …

We relate commutative algebras in braided tensor categories to braid-reversed tensor
equivalences, motivated by vertex algebra representation theory. First, for C a braided …

A bstract We formulate a conjectural relation between the category of line defects in
topologically twisted 3d\(\mathcal {N}\)= 4 supersymmetric quantum field theories and …