Gauge Structure of Vacuum String Field Theory

TL;DR

This paper investigates the gauge structure of vacuum string field theory around a D-brane, revealing anomalies in gauge transformations and challenges in deriving the transversality condition for massless vector modes.

Contribution

It uncovers the anomaly-induced gauge transformation and the difficulty in obtaining the transversality condition within the gauge structure of the theory.

Findings

Gauge transformation is induced as an anomaly involving infinities and infinitesimals.

Transversality condition cannot be derived even considering anomaly contributions.

Singularities at the eigenvalue distribution edge affect the gauge structure analysis.

Abstract

We study the gauge structure of vacuum string field theory expanded around the D-brane solution, namely, the gauge transformation and the transversality condition of the massless vector fluctuation mode. We find that the gauge transformation on massless vector field is induced as an anomaly; an infinity multiplied by an infinitesimal factor. The infinity comes from the singularity at the edge of the eigenvalue distribution of the Neumann matrix, while the infinitesimal factor from the violation of the equation of motion of the fluctuation modes due to the regularization for the infinity. However, the transversality condition cannot be obtained even if we take into account the anomaly contribution.