SDiff(2) KP hierarchy

Details SDiff(2) KP hierarchy SDiff(2) KP hierarchy

1991-12-18

arxiv.org/abs/hep-th/9112046v2

Int.J.Mod.Phys. A7S1B (1992) 889-922

Physics

High Energy Physics

High Energy Physics - Theory

34 pages (errors in earlier and published versions are corrected)

Scientific paper

10.1142/S0217751X92004099

An analogue of the KP hierarchy, the SDiff(2) KP hierarchy, related to the group of area-preserving diffeomorphisms on a cylinder is proposed. An improved Lax formalism of the KP hierarchy is shown to give a prototype of this new hierarchy. Two important potentials, $S$ and $\tau$, are introduced. The latter is a counterpart of the tau function of the ordinary KP hierarchy. A Riemann-Hilbert problem relative to the group of area-diffeomorphisms gives a twistor theoretical description (nonlinear graviton construction) of general solutions. A special family of solutions related to topological minimal models are identified in the framework of the Riemann-Hilbert problem. Further, infinitesimal symmetries of the hierarchy are constructed. At the level of the tau function, these symmetries obey anomalous commutation relations, hence leads to a central extension of the algebra of infinitesimal area-preserving diffeomorphisms (or of the associated Poisson algebra).

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