Vertex algebras and Hodge structures

We compare the context of Hodge structures with that of vertex algebras of conformal field theory. Vertex algebras appear as the highest weight representations of infinite dimensional Lie algebras. A correspondence between Higgs bundles and opers already is known as non-abelian Hodge theorem due to...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-12
Main Author: Rahmati, Mohammad Reza
Format: Article
Language:English
Subjects:
Algebra
Field theory
Fields (mathematics)
Homomorphisms
Isomorphism
Lie groups
Modules
Number theory
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We compare the context of Hodge structures with that of vertex algebras of conformal field theory. Vertex algebras appear as the highest weight representations of infinite dimensional Lie algebras. A correspondence between Higgs bundles and opers already is known as non-abelian Hodge theorem due to C. Simpson. The Beilinson-Bernstein localization (correspondence) also compares the context of variation of Hodge structure with that of highest weight modules over flag manifolds of semisimple Lie groups. A more general analogue of the Bernstein correspondence over a local manifold can also be formulted in the context of geometric Langlands correspondence. We discuss a generalized version of Harish-Chandra modules called Wakimoto modules and a generalized Harish-Chandra homomorphism. This text is mainly an expository discussion with a new insight toward the two concepts. We conclude with an explanation of geometric Langlands correspondence.
ISSN:2331-8422