Field Redefinitions in String Theory as a Solution Generating Technique

TL;DR

The paper identifies a new invariance in string theory's beta-function equations that acts as a solution generating technique by shifting the dilaton and scaling the lapse, enabling transformations between solutions with different cosmological constants.

Contribution

It introduces an additional invariance related to field redefinitions in string theory that can generate new solutions from existing ones, including those with different cosmological constants.

Findings

Field redefinitions map solutions with non-zero to zero cosmological constant.

The invariance preserves the form of beta-function equations but alters the effective action.

Examples include black holes and black strings illustrating the solution-generating technique.

Abstract

The purpose of this work is to show that there exists an additional invariance of the $\beta$-function equations of string theory on $d+1$-dimensional targets with $d$ toroidal isometries. It corresponds to a shift of the dilaton field and a scaling of the lapse function, and is reminiscent of string field redefinitions. While it preserves the form of the $\beta$-function equations, it changes the effective action and the solutions. Thus it can be used as a solution generating technique. It is particularly interesting to note that there are field redefinitions which map solutions with non-zero string cosmological constant to those with zero cosmological constant. Several simple examples involving two- and three-dimensional black holes and black strings are provided to illustrate the role of such field redefinitions.