On the Relation of Four-Dimensional N=2,4 -- Supersymmetric String Backgrounds to Integrable Models

Details On the Relation of Four-Dimensional N=2,4 -- Supersymmetric String Backgrounds to Integrable Models On the Relation of Four-Dimensional N=2,4 -- Supersymmetric String Backgrounds to Integrable Models

1994-11-14

arxiv.org/abs/hep-th/9411095v2

Phys.Lett.B345:220-226,1995

Physics

High Energy Physics

High Energy Physics - Theory

10 pages,latex (references added)

Scientific paper

10.1016/0370-2693(94)01636-Q

In this letter we discuss the relation of four-dimensional, $N=2$ supersymmetric string backgrounds to integrable models. In particular we show that non-K\"ahlerian gravitational backgrounds with one $U(1)$ isometry plus non-trivial antisymmetric tensor and dilaton fields arise as the solutions of the Liouville equation or, for the case of vanishing central charge deficit, as the solutions of the continual Toda equation. When performing an Abelian duality transformation, a particular class of solutions of the continual Toda equation leads to the well-known gravitational Eguchi-Hanson instanton background with self-dual curvature tensor.

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