Free Field Realisation of the Chiral Universal Centraliser.

In the TQFT formalism of Moore-Tachikawa for describing Higgs branches of theories of class , the space associated to the unpunctured sphere in type is the universal centraliser , where . In more physical terms, this space arises as the Coulomb branch of pure gauge theory in three dimensions with gauge group , the Langlands dual. In the analogous formalism for describing chiral algebras of class , the vertex algebra associated to the sphere has been dubbed the .

Twisted Chiral Algebras of Class and Mixed Feigin-Frenkel Gluing.

The correspondence between four-dimensional superconformal field theories and vertex operator algebras, when applied to theories of class , leads to a rich family of VOAs that have been given the monicker . A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in Arakawa (Chiral algebras of class and Moore-Tachikawa symplectic varieties, 2018. arXiv:1811.