The Equality of Solutions in Vacuum String Field Theory

TL;DR

This paper provides analytical proofs that various solutions in vacuum string field theory, including matter, ghost, and tachyon states, are equivalent to the sliver state, confirming their consistency within the theory.

Contribution

It offers the first analytical proofs establishing the equivalence of key solutions to the sliver state in vacuum string field theory, using recent techniques by Okuyama.

Findings

Matter solution is the matter sliver state.

Ghost solution is the sliver state in twisted ghost CFT.

Tachyon candidate state matches the Rastelli-Sen-Zwiebach construction.

Abstract

We analytically prove that the matter solution of vacuum string field theory constructed by Kostelecky and Potting is the matter sliver state. We also give an analytical proof that the ghost solution by Hata and Kawano is the sliver state in the twisted ghost CFT. It is also proved that the candidate state for the tachyon proposed by Hata and Kawano can be identified with the state constructed by Rastelli, Sen and Zwiebach using CFT. Our proofs are based on the techniques recently developed by Okuyama.