Field Redefinitions in String Theory as a Solution Generating Technique

The purpose of this work is to show that there exists an additional invariance of the βfunction 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 β-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 twoand three-dimensional black holes and black strings are provided to illustrate the role of such field redefinitions. Submitted to Phys. Lett. B Vigorous research in string theory in non-trivial backgrounds in the past few years has yielded a number of novel approaches for the construction and classification of string vacua. One such method is known as string duality, or twisting procedure, or O(d, d+n) boosting (in presence of n independent gauge fields) [1]-[7]. It employs the fact that many string solutions posses toroidal symmetries associated with the appearance of commuting translational Killing vectors spanning the tangent-space basis. At the level of the effective field theory on target space, the symmetry takes a very simple form. One can rewrite the effective action in terms of the independent degrees of freedom, after dimensional reduction a là Kaluza-Klein, and extract the O(d, d + n) group as a part of the full invariance group of the theory. Although the action and the equations of motion (the β-function equations) are invariant under this group, the initial conditions are not. Thus under an O(d, d+ n) transformation a solution to the equations of motion transforms, in principle, to a different solution. (One has to remember that O(d, d+n) transformations contain diffeomorphisms and gauge transformations which have to be factored out, since they don’t change solutions [4]. ) In this letter, I will show that there exists another transformation which leaves the β-function equations form-invariant, although the action and the solutions are changed. It is realized by shifting the dilaton field and scaling the lapse function, and in its appearance is similar to a string field redefinition, which does not change the physics of the fundamental string [8]. For this reason, and for the sake of brevity, I will tentatively refer to it as a ”field redefinition”, dropping the term ”string” to indicate that in general they are different. Therefore, in what follows, by field redefinition it is meant a transformation in the above sense, while the label string field redefinition refers to the conventional ambiguity of string theory. This field redefinition is not completely arbitrary, for one must require that the transformation preserve the form of the lowest order β-function equations while changing solutions. Viewed as a consistency condition, this imposes a constraint on the field redefinition parameters. The constraint admits non-trivial solutions for all string configurations from the class considered here, namely with all but one toroidal isometries. The field redefinitions