Virasoro Algebra and O(N) Sigma Model

TL;DR

This paper explores the structure of the Virasoro algebra within the O(N) sigma-model, providing a local expansion approach to analyze the vacuum functional and deriving a modified algebra with a central charge term.

Contribution

It introduces a local expansion method for the sigma-model vacuum functional and derives a modified Virasoro algebra with a central charge term up to second order.

Findings

Derived a modified Virasoro algebra for the O(N) sigma-model.

Calculated the operator-like central charge term up to second order.

Provided a framework for analyzing slowly varying fields in the sigma-model.

Abstract

Within the framework of a local expansion of the logarithm of the O(N) sigma-model vacuum functional, valid for slowly varying fields, the modified Virasoro algebra is studied. The operator-like central charge term is given, up to second order, for a general functional.