Associated varieties and Higgs branches (a survey)

Abstract

Associated varieties of vertex algebras are analogue of the associated varieties of primitive ideals of the universal enveloping algebras of semisimple Lie algebras. They not only capture some of the important properties of vertex algebras but also have interesting relationship with the Higgs branches of four-dimensional $N=2$ superconformal field theories (SCFTs). As a consequence, one can deduce the modular invariance of Schur indices of 4d $N=2$ SCFTs from the theory of vertex algebras.

To appear in conference proceedings for AMS Special Session on Vertex Algebras and Geometry. v2: added references

References in corpus (1)

• Vertex operator algebras of Argyres-Douglas theories from M5-branes

Cited by in corpus (3)

• Logarithmic W-algebras and Argyres-Douglas theories at higher rank
• Singular support of a vertex algebra and the arc space of its associated scheme
• Arc spaces and chiral symplectic cores