Virasoro algebra in $K$-space

TL;DR

This paper presents a new representation of the Virasoro algebra within open string field theory, using vector fields on the $K$-space, and explores its implications for various D-brane backgrounds.

Contribution

It introduces a novel Virasoro algebra representation in $K$-space and analyzes its behavior in different open string backgrounds, including multiple D-branes.

Findings

Virasoro generators act as vector fields on $K$-space.

Different behaviors observed around $K=0$ for various D-brane configurations.

Representation extends to nontrivial open string backgrounds.

Abstract

We introduce a novel representation of Virasoro algebra in open string field theory. Elements of the algebra are vector fields on the $K$-space, where $K$ is the string field that generates a world sheet strip in sliver frame. The generators introduce a global symmetry of open string field theory. We also derive a representation of Virasoro algebra for nontrivial open string background described by the formal pure gauge solution. Generators for 0, 1 and 2 D-branes are explicitly studied and different behaviors around $K=0$ are observed.