Exact Models of Extremal Dyonic 4D Black Hole Solutions of Heterotic String Theory

TL;DR

This paper constructs exact conformal field theories for extremal dyonic black holes in heterotic string theory, ensuring quantum consistency and generalizing known models with new solutions.

Contribution

It introduces a novel class of exact (0,2) supersymmetric CFT models for extremal dyonic black holes, expanding the landscape of heterotic string solutions.

Findings

Constructed consistent (0,2) supersymmetric models with gauged U(1) subgroups.

Generalized known heterotic backgrounds, including the Giddings-Polchinski-Strominger model.

Presented a detailed example of a mixed radial and angular theory leading to a dyonic Taub-NUT-like solution.

Abstract

Families of exact $(0,2)$ supersymmetric conformal field theories of magnetically and electrically charged extremal 4D black hole solutions of heterotic string theory are presented. They are constructed using a $(0,1)$ supersymmetric $SL(2,R)\times SU(2)$ WZW model where anomalously embedded $U(1)\times U(1)$ subgroups are gauged. Crucial cancelations of the $U(1)$ anomalies coming from the supersymmetric fermions, the current algebra fermions and the gauging ensure that there is a consistency of these models at the quantum level. Various 2D models, which may be considered as building blocks for extremal 4D constructions, are presented. They generalise the class of 2D models which might be obtained from gauging $SL(2,R)$ and coincide with known heterotic string backgrounds. The exact conformal field theory presented by Giddings, Polchinski and Strominger describing the angular sector of the extremal magnetically charged black hole is a special case of this construction. An example where the radial and angular theories are mixed non--trivially is studied in detail, resulting in an extremal dilatonic Taub--NUT--like dyon.