The Zero Tension Limit of The Virasoro Algebra and the Central Extension

TL;DR

This paper explores how the Virasoro algebra simplifies to the null string algebra in the zero tension limit, showing the central extension disappears as tension approaches zero, providing insights into tensionless string theory.

Contribution

It reformulates the Virasoro algebra for the bosonic string to analyze its behavior in the zero tension limit, revealing the null string algebra and the vanishing of the central extension.

Findings

Virasoro algebra reduces to null string algebra at zero tension

Central extension vanishes as tension approaches zero

Provides a framework for tensionless string analysis

Abstract

We argue that the Virasoro algebra for the closed bosonic string can be cast in a form which is suitable for the limit of vanishing string tension. In this form the limit of the Virasoro algebra gives the null string algebra. The anomalous central extension is seen to vanish as well when $T\to 0$.