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arXiv · hep-th/9302057

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

J. M. Figueroa-O'Farrill·S. Stanciu
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Abstract

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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J. M. Figueroa-O'Farrill, S. Stanciu. 2020-10-16. On a New Supersymmetric KdV Hierarchy in $2{-}d$ Quantum Supergravity. https://doi.org/10.1016/0370-2693(93)90326-d

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