On a New Supersymmetric KdV Hierarchy in $2{-}d$ Quantum Supergravity

Details On a New Supersymmetric KdV Hierarchy in $2{-}d$ Quantum Supergravity On a New Supersymmetric KdV Hierarchy in $2{-}d$ Quantum Supergravity

1993-02-14

arxiv.org/abs/hep-th/9302057v1

Phys.Lett. B316 (1993) 282-290

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, Plain TeX, BONN-HE-93-007

Scientific paper

10.1016/0370-2693(93)90326-D

Recently a new supersymmetric extension of the KdV hierarchy has appeared in a matrix-model-inspired approach to $2{-}d$ quantum supergravity. Here we prove that this hierarchy is essentially the KdV hierarchy, where the KdV field is now replaced by an even superfield. This allows us to find the conserved charges and the bihamiltonian structure, and to prove its integrability. We also extend the hierarchy by odd flows in a supersymmetric fashion.

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