Some exact computations on the twisted butterfly state in string field theory

TL;DR

This paper provides an exact conformal field theory description of the twisted butterfly state in vacuum string field theory, demonstrating conditions under which its energy density remains finite and analyzing the impact of subleading terms.

Contribution

It introduces a conformal field theory framework with zero central charge for the twisted butterfly state and computes relevant quantities exactly, clarifying energy density finiteness conditions.

Findings

Energy density can be finite in the limit.

Subleading terms can significantly contribute to energy density.

Conformal anomaly issues are addressed with a c=0 CFT description.

Abstract

The twisted butterfly state solves the equation of motion of vacuum string field theory in the singular limit. The finiteness of the energy density of the solution is an important issue, but possible conformal anomaly resulting from the twisting has prevented us from addressing this problem. We present a description of the twisted regulated butterfly state in terms of a conformal field theory with a vanishing central charge which consists of the ordinary bc ghosts and a matter system with c=26. Various quantities relevant to vacuum string field theory are computed exactly using this description. We find that the energy density of the solution can be finite in the limit, but the finiteness depends on the subleading structure of vacuum string field theory. We further argue, contrary to our previous expectation, that contributions from subleading terms in the kinetic term to the energy density can be of the same order as the contribution from the leading term which consists of the midpoint ghost insertion.