The Nichols algebra of screenings

TL;DR

This paper explores the algebraic structure of screening operators in two-dimensional conformal field theory, proposing Nichols algebras as a key tool to understand the representation categories of vertex-operator algebras in logarithmic CFT models.

Contribution

It introduces the use of Nichols algebras and Yetter-Drinfeld modules as algebraic counterparts to screening operators in logarithmic CFT, extending the Kazhdan-Lusztig duality.

Findings

Establishes a connection between Nichols algebras and screening operators in CFT.

Proposes a braided category framework for logarithmic CFT models.

Provides a new algebraic perspective on vertex-operator algebra representations.

Abstract

Two related constructions are associated with screening operators in models of two-dimensional conformal field theory. One is a local system constructed in terms of the braided vector space X spanned by the screening species in a given CFT model and the space of vertex operators Y and the other is the Nichols algebra B(X) and the category of its Yetter--Drinfeld modules, which we propose as an algebraic counterpart, in a "braided" version of the Kazhdan--Lusztig duality, of the representation category of vertex-operator algebras realized in logarithmic CFT models.