Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-07-16
J.Math.Phys. 36 (1995) 3574-3607
Physics
High Energy Physics
High Energy Physics - Theory
50 pages, (Changes: a few references are added; numbering of formulas are slightly modified)
Scientific paper
10.1063/1.530983
A higher dimensional analogue of the dispersionless KP hierarchy is introduced. In addition to the two-dimensional ``phase space'' variables $(k,x)$ of the dispersionless KP hierarchy, this hierarchy has extra spatial dimensions compactified to a two (or any even) dimensional torus. Integrability of this hierarchy and the existence of an infinite dimensional of ``additional symmetries'' are ensured by an underlying twistor theoretical structure (or a nonlinear Riemann-Hilbert problem). An analogue of the tau function, whose logarithm gives the $F$ function (``free energy'' or ``prepotential'' in the contest of matrix models and topological conformal field theories), is constructed. The infinite dimensional symmetries can be extended to this tau (or $F$) function. The extended symmetries, just like those of the dispersionless KP hierarchy, obey an anomalous commutation relations.
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