On the solutions to the string equation

Details On the solutions to the string equation On the solutions to the string equation

1991-09-10

arxiv.org/abs/hep-th/9109015v1

Mod.Phys.Lett. A6 (1991) 2713-2726

Physics

High Energy Physics

High Energy Physics - Theory

15 pp (revised version)

Scientific paper

10.1142/S0217732391003171

The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are differential operators is described.It is shown that there exists one-to-one correspondence between this set and the set of pairs of commuting differential operators.This fact permits us to describe the set of solutions to the string equation in terms of moduli spa- ces of algebraic curves,however the direct description is much simpler. Some results are obtained for the superanalog to the string equation where $P$ and $Q$ are considered as superdifferential operators. It is proved that this equation is invariant with respect to Manin-Radul, Mulase-Rabin and Kac-van de Leur KP-hierarchies.

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