The Perturbative Spectrum of the Dressed Sliver

TL;DR

This paper investigates the fluctuation spectrum of the dressed sliver in Vacuum String Field Theory, revealing how dressing enforces transversality, manages singular modes, and reproduces the expected brane tension ratios.

Contribution

It provides a detailed analysis of the fluctuation spectrum of the dressed sliver, including the derivation of the tachyon wave function and the role of dressing in physical conditions.

Findings

Dressing enforces transversality on the massless vector.

A string midpoint regulator handles singular modes.

The energy density ratio matches the three-tachyon coupling prediction.

Abstract

We analyze the fluctuations of the dressed sliver solution found in a previous paper, hep-th/0311198, in the operator formulation of Vacuum String Field Theory. We derive the tachyon wave function and then analyze the higher level fluctuations. We show that the dressing is responsible for implementing the transversality condition on the massless vector. In order to consistently deal with the singular $k=0$ mode we introduce a string midpoint regulator and we show that it is possible to accommodate all the open string states among the solutions to the linearized equations of motion. We finally show how the dressing can give rise to the correct ratio between the energy density of the dressed sliver and the brane tension computed via the three-tachyons-coupling.