Two-Dimensional Dilaton Gravity Black Hole Solution for $N=2$ Superstring Theory

TL;DR

This paper demonstrates that the $N=8$ self-dual supergravity theory, related to $N=2$ superstring theory, can incorporate two-dimensional dilaton gravity black hole solutions through dimensional reductions, revealing deep connections between superstring theory and lower-dimensional black holes.

Contribution

It shows how two-dimensional black hole solutions can be embedded into $N=8$ supergravity, linking superstring theory with lower-dimensional gravitational solutions and integrable systems.

Findings

Black hole solutions embedded in $N=8$ supergravity.

Dilaton field arises from scalar in $SO(8)$ representation.

Connections between $N=2$ superstring and 2D black holes.

Abstract

We show that $N=8$ {\it self-dual} supergravity theory, which is the consistent background for $N=2$ closed superstring theory in $2+2\-$dimensions, can accommodate the recently discovered two-dimensional dilaton gravity black hole solution, {\it via} appropriate dimensional reductions and truncations. Interestingly, the usual dilaton field in this set of solutions emerges from the scalar field in the ${\bf 70}\-$dimensional representation of an intrinsic global $SO(8)$ group. We also give a set of exact solutions, which can be interpreted as the dilaton field on Eguchi-Hanson gravitational instanton background, realized in an $N=1$ self-dual supergravity theory. This suggests that the $N=2$ superstring has a close (even closer) relationship with the two-dimensional black hole solution, which was originally developed in the context of bosonic string and $N=1$ superstring. Our result also provides supporting evidence for the conjecture that the $N=2$ superstring theory is the ``master theory'' of supersymmetric integrable systems in lower-dimensions.