Stationary BPS solutions to dilaton-axion gravity

TL;DR

This paper classifies stationary BPS solutions in dilaton-axion gravity using a geometric approach, revealing new solution classes with regular string metrics and exploring their symmetry properties.

Contribution

It provides a detailed classification of BPS solutions in dilaton-axion gravity, including new asymptotically flat solutions with minimal charge constraints and regular string metrics.

Findings

Classified BPS solutions via null geodesics on coset spaces.

Derived general multicenter solutions in a straightforward manner.

Discovered new asymptotically flat solutions with minimal charge constraints.

Abstract

Stationary four-dimensional BPS solutions to gravity coupled bosonic theories admitting a three-dimensional sigma-model representation on coset spaces are interpreted as null geodesics of the target manifold equipped with a certain number of harmonic maps. For asymptotically flat (or Taub-NUT) space-times such geodesics can be directly parametrized in terms of charges saturating the Bogomol'nyi-Gibbons-Hull bound, and classified according to the structure of related coset matrices. We investigate in detail the ``dilaton-axion gravity'' with one vector field, and show that in the space of BPS solutions an $SO(1,2) \times SO(2)$ classical symmetry is acting. Within the present formalism the most general multicenter (IWP/Taub-NUT dyon) solutions are derived in a simple way. We also discover a large new class of asymptotically flat solutions for which the dilaton and axion charges are constrained only by the BPS bound. The string metrics for these solutions are generically regular. Both the IWP class and the new class contain massless solutions.