Two–dimensional Dilaton Gravity Black Hole Solution for N = 2 Superstring Theory

We show that N = 8 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, via appropriate dimensional reductions and truncations. Interestingly, the usual dilaton field in this set of solutions emerges from the scalar field in the 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 su-pergravity 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.