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Third order differential equations with fixed critical points
Cataloged from PDF version of article.The singular point analysis of third order ordinary differential equations which are algebraic in y and y′ is presented. Some new third order ordinary differential equations that pass the Painlevé test as well as the known ones are found. © 2008 Elsevier Inc. All rights reserved
DV and WDVV
We prove that the quasiclassical tau-function of the multi-support solutions
to matrix models, proposed recently by Dijkgraaf and Vafa to be related to the
Cachazo-Intrilligator-Vafa superpotentials of the N=1 supersymmetric Yang-Mills
theories, satisfies the Witten-Dijkgraaf-Verlinde-Verlinde equations.Comment: 15 pages, 2 figure
Second and Third Order Observables of the Two-Matrix Model
In this paper we complement our recent result on the explicit formula for the
planar limit of the free energy of the two-matrix model by computing the second
and third order observables of the model in terms of canonical structures of
the underlying genus g spectral curve. In particular we provide explicit
formulas for any three-loop correlator of the model. Some explicit examples are
worked out.Comment: 22 pages, v2 with added references and minor correction
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