Vacuum string field theory without matter-ghost factorization

TL;DR

This paper demonstrates that vacuum string field theory with a singular kinetic operator can be derived from a regular theory via field redefinition, providing evidence for finite D-brane energy densities and correct tension ratios.

Contribution

It shows how to obtain the singular vacuum string field theory from a regular theory and analyzes solutions without matter-ghost factorization, confirming physical D-brane properties.

Findings

Energy density of D25-brane is finite and well-defined.

Solutions for different D-branes can be constructed by boundary conditions.

Ratios of D-brane tensions are correctly reproduced.

Abstract

We show that vacuum string field theory with the singular kinetic operator conjectured by Gaiotto, Rastelli, Sen and Zwiebach can be obtained by field redefinition from a regular theory constructed by Takahashi and Tanimoto. We solve the equation of motion both by level truncation and by a series expansion using the regulated butterfly state, and we find evidence that the energy density of a D25-brane is well defined and finite. Although the equation of motion naively factorizes into the matter and ghost sectors in the singular limit, subleading terms in the kinetic operator are relevant and the factorization does not strictly hold. Nevertheless, solutions corresponding to different D-branes can be constructed by changing the boundary condition in the boundary conformal field theory formulation of string field theory, and ratios of D-brane tensions are shown to be reproduced correctly.