On the Background Independence of String Field Theory: III. Explicit Field Redefinitions

TL;DR

This paper constructs explicit field redefinitions relating string field theories based on conformal field theories connected by marginal perturbations, focusing on quadratic and cubic terms, and discusses their equivalence.

Contribution

It provides explicit methods for field redefinitions between string field theories around related backgrounds, extending understanding of their equivalence.

Findings

Explicit redefinitions for quadratic and cubic terms are constructed.

Examples demonstrate the relation between theories with different conformal backgrounds.

Discussion on the potential for higher-point vertex redefinitions and theory equivalences.

Abstract

Given two conformal field theories related to each other by a marginal perturbation, and string field theories constructed around such backgrounds, we show how to construct explicit redefinition of string fields which relate these two string field theories. The analysis is carried out completely for quadratic and cubic terms in the action. Although a general proof of existence of field redefinitions which relate higher point vertices is not given, specific examples are discussed. Equivalence of string field theories formulated around two conformal field theories which are not close to each other, but are related to each other by a series of marginal deformations, is also discussed. The analysis can also be applied to study the equivalence of different formulation of string field theories around the same background.