CFT Description of Identity String Field: Toward Derivation of the VSFT Action

TL;DR

This paper defines the identity string field within conformal field theory, providing a rigorous framework that supports deriving the vacuum string field theory action from the cubic string field theory.

Contribution

It introduces a CFT-based definition of the identity string field and demonstrates its role in deriving the VSFT action from cubic string field theory.

Findings

Identity string field is defined as a surface state in CFT.

The generalized gluing and resmoothing theorem is used for computations.

Explicit classical solutions are constructed supporting the VSFT conjecture.

Abstract

We concretely define the identity string field as a surface state and deal with it consistently in terms of conformal field theory language, never using its formal properties nor oscillator representation of it. The generalized gluing and resmoothing theorem provides us with a powerful computational tool which fits into our framework. Among others, we can prove that in some situations the identity state defined this way actually behaves itself like an identity element under the *-product. We use these CFT techniques to give an explicit expression of the classical solution in the ordinary cubic string field theory having the property that the conjectured vacuum string field theory action arises when the cubic action is expanded around it.