D-particles,matrix integrals and KP hierarchy |
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| Institution: | 2. CERN, Theory Division, 1211 Geneva 23, Switzerland;3. C.E.A. - Saclay, Service de Physique Théorique, F-91191 Gif-Sur-Yvette, France;4. Institute of Theoretical and Experimental Physics, 117259, Moscow, Russia;5. Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA;1. School of Mathematics and Applied Statistics, University of Wollongong, Northfields Ave., Wollongong NSW 2522, Australia;2. School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, Scotland, EH9 3FD, UK;1. Laboratory of Electronics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon;2. Department of Physics, Higher Teacher Training College Yaounde, University of Yaounde I, P.O. Box 47, Yaounde, Cameroon;3. Department of Physics, Faculty of Science, Moulay Ismail University, P.O. Box. 1120, Meknes, Morocco;4. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon;5. Centre d׳Excellence Africain des Technologies de l׳Information et de la Communication (CETIC), Université de Yaoundé I, Cameroon |
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| Abstract: | We study the regularized correlation functions of the light-like coordinate operators in the reduction to zero dimensions of the matrix model describing D-particles in four dimensions. We investigate in great detail the related matrix model originally proposed and solved in the planar limit by J. Hoppe. It also gives the solution of the problem of 3-coloring of planar graphs. We find interesting strong/weak 't Hooft coupling dependence. The partition function of the grand canonical ensemble turns out to be a tau-function of KP hierarchy. As an illustration of the method we present a new derivation of the large-N and double-scaling limits of the one-matrix model with cubic potential. |
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