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Geometry of the string equations. (English) Zbl 0727.35134

This paper presents an attempt to construct a mathematical framework for the string equations of Hermitian and unitary 2D matrix models. The physical parameters defining the string equations are interpreted as moduli of meromorphic gauge fields and the compatibility conditions can be interpreted as defining a “quantum” Riemann space. As an application of this formalism some properties of the Brezin-Marinari-Parisi solutions [see E. Brezin, E. Marinari and G. Parisi, A non- perturbative ambiguity free solution of a string model, ROM 2F 90-09] are discussed and a connection to twistor theory is briefly mentioned.

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
81R25 Spinor and twistor methods applied to problems in quantum theory
35Q53 KdV equations (Korteweg-de Vries equations)
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