Charged Dual String Vacua from Interacting Rotating Black Holes Via Discrete and Nonlinear Symmetries

TL;DR

This paper explores how discrete and nonlinear symmetries in heterotic string theory can generate and relate various charged and neutral black hole solutions, naked singularities, and string vacua.

Contribution

It introduces a method to generate charged string vacua from neutral backgrounds using nonlinear symmetries like the Harrison transformation.

Findings

Discrete symmetries relate different black hole and singularity solutions.

Nonlinear Harrison transformation charges neutral backgrounds, producing charged solutions.

The framework connects rotating and static black holes with various field configurations.

Abstract

Using the stationary formulation of the toroidally compactified heterotic string theory in terms of a pair of matrix Ernst potentials we consider the four-dimensional truncation of this theory with no U(1) vector fields excited. Imposing one time-like Killing vector permits us to express the stationary effective action as a model in which gravity is coupled to a matrix Ernst potential which, under certain parametrization, allows us to interpret the matter sector of this theory as a double Ernst system. We generate a web of string vacua which are related to each other via a set of discrete symmetries of the effective action (some of them involve S-duality transformations and possess non-perturbative character). Some physical implications of these discrete symmetries are analyzed and we find that, in some particular cases, they relate rotating black holes coupled to a dilaton with no Kalb--Ramond field, static black holes with non-trivial dilaton and antisymmetric tensor fields, and rotating and static naked singularities. Further, by applying a nonlinear symmetry, namely, the so-called normalized Harrison transformation, on the seed field configurations corresponding to these neutral backgrounds, we recover the U(1)^n Abelian vector sector of the four-dimensional action of the heterotic string, charging in this way the double Ernst system which corresponds to each one of the neutral string vacua, i.e., the stationary and the static black holes and the naked singularities.