Exact time-localized solutions in Vacuum String Field Theory

TL;DR

This paper constructs localized time-dependent solutions in Vacuum String Field Theory by applying a double Wick rotation to Euclidean lump solutions, analyzing their behavior in different energy regimes and relating them to rolling tachyon solutions.

Contribution

It introduces a novel method to obtain time-localized solutions in VSFT using Wick rotation of lump solutions, bridging static and dynamic string configurations.

Findings

Localized time profiles are achieved after inverse Wick rotation.

Solutions exhibit similarities with rolling tachyon in high energy limit.

The approach works in both low energy and tensionless regimes.

Abstract

We address the problem of finding star algebra projectors that exhibit localized time profiles. We use the double Wick rotation method, starting from an Euclidean (unconventional) lump solution, which is characterized by the Neumann matrix being the conventional one for the continuous spectrum, while the inverse of the conventional one for the discrete spectrum. This is still a solution of the projector equation and we show that, after inverse Wick-rotation, its time profile has the desired localized time dependence. We study it in detail in the low energy regime (field theory limit) and in the extreme high energy regime (tensionless limit) and show its similarities with the rolling tachyon solution.