N=2 Supersymmetry and String-Loop Corrected Magnetic Black Holes

TL;DR

This paper investigates string-loop corrections to magnetic black holes in N=2 supersymmetric theories derived from heterotic string compactifications, analyzing how quantum effects modify classical solutions near the black hole core.

Contribution

It provides the first-order string-loop corrected solutions for magnetic black holes in N=2 supergravity, including metric and dilaton modifications near the singularity.

Findings

Loop corrections become significant at small distances from the black hole center.

Quantum corrections may smooth out the classical singularity.

The corrected solutions differ notably from the tree-level black hole solutions.

Abstract

We study string-loop corrections to magnetic black hole. Four-dimensional theory is obtained by compactification of the heterotic string theory on the manifold $K3\times T^2$ or on a suitable orbifold yielding N=1 supersymmetry in 6D. The resulting 4D theory has N=2 local supersymmetry. Prepotential of this theory receives only one-string-loop correction. The tree-level gauge couplings are proportional to the inverse effective string coupling and decrease at small distances from the center of magnetic black hole, so that loop corrections to the gauge couplings are important in this region. We solve the system of spinor Killing equations (conditions for the supersymmetry variations of the fermions to vanish) and Maxwell equations. At the string-tree level, we reproduce the magnetic black hole solution which can be also obtained by solving the system of the Einstein-Maxwell equations and the equations of motion for the moduli. String-loop corrections to the tree-level solution are calculated in the first order in string coupling. The resulting corrections to the metric and dilaton are large at small distances from the center of the black hole. Possible smearing of the singularity at the origin by quantum corrections is discussed.