1994/07/31 by Kanehisa Takasaki · 16 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Conformal field theory #Conformal map #Context (archaeology) #Gravitational singularity #Hierarchy #Homogeneous space #Integrable system #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Ramanujan tau function #Twistor theory #hep-th #nlin.SI #solv-int
paper · pdf · doi:10.1063/1.530983
published in Journal of Mathematical Physics 36(7), 3574-3607 (American Institute of Physics) · 50 pages, (Changes: a few references are added; numbering of formulas are slightly modified)
arxiv created 1994/08/03 · openalex publication_date 1995/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 context 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.