Gauge transformations on a D-brane in Vacuum String Field Theory

TL;DR

This paper analyzes gauge transformations of a vector state on a D-brane within vacuum string field theory, revealing the gauge freedom in polarization components and discussing challenges in formulating a gauge-invariant action.

Contribution

It demonstrates that all but one polarization component are gauge degrees of freedom and connects string field gauge transformations to U(1) gauge symmetry.

Findings

Most polarization components are gauge degrees of freedom.

Gauge transformations reproduce U(1) gauge symmetry.

Difficulty in constructing a gauge-invariant vector field action.

Abstract

We study gauge transformations of the Hata-Kawano vector state on a D25-brane in the framework of vacuum string field theory. We show that among the infinite number of components of the polarization vector, all the components except one spacetime vector degree of freedom are gauge freedom, and give string field gauge transformations reproducing gauge transformations of the constant modes of the U(1) gauge field. These gauge transformations can be used to fix the normalization of the vector field. We also discuss a difficulty in obtaining a gauge invariant action of the vector field. Our arguments rely on the factorization ansatz of gauge transformations.