Logarithmic modules for chiral differential operators of nilmanifolds

TL;DR

This paper explicitly constructs the vertex algebra of twisted chiral differential operators on nilmanifolds and introduces logarithmic modules using generalized vertex operators involving Jacobi theta functions.

Contribution

It provides the first explicit construction of logarithmic modules for chiral differential operators on nilmanifolds, extending the theory with new examples.

Findings

Explicit description of vertex algebra on nilmanifolds

Construction of logarithmic modules using theta functions

Provides new examples of logarithmic vertex algebra modules

Abstract

We describe explicitly the vertex algebra of (twisted) chiral differential operators on certain nilmanifolds and construct their logarithmic modules. This is achieved by generalizing the construction of vertex operators in terms of exponentiated scalar fields to Jacobi theta functions naturally appearing in these nilmanifolds. This provides with a non-trivial example of logarithmic vertex algebra modules, a theory recently developed by Bakalov.