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• W3098253185 abstract "We solve Virasoro constraints on the KP hierarchy in terms of minimal conformal models. The constraints we start with are implemented by the Virasoro generators depending on a background charge Q. Then the solutions to the constraints are given by the theory which has the same field content as the David-Distler-Kawai theory: it consists of a minimal matter scalar with background charge Q, dressed with an extra “Liouville” scalar. In particular, the Virasoro-constrained τ-function is related to the correlator of a product of (dressed) “21” operators. The construction is based on a generalization of the Kontsevich parametrization of the KP times achieved by introducing into it Miwa parameters which depend on the value of Q. Under the thus defined Kontsevich-Miwa transformation, the Virasoro constraints are proven to be equivalent to a master equation depending on the parameter Q. The master equation is further identified with the decoupling equation corresponding to a null vector at level 2. We conjecture that higher-level decoupling equations are similarly related to constraints on the KP τ-function. We also consider the master equation for the N-reduced KP hierarchies. Several comments are made on a possible relation between the generalized master equation and scaled Kontsevich-type matrix integrals, and on the form the equation takes in higher genera." @default.
• W3098253185 created "2020-11-23" @default.
• W3098253185 creator A5050703737 @default.
• W3098253185 date "1992-11-01" @default.
• W3098253185 modified "2023-09-26" @default.
• W3098253185 title "Solving Virasoro constraints on integrable hierarchies via the Kontsevich-Miwa transform" @default.
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• W3098253185 doi "https://doi.org/10.1016/0550-3213(92)90178-e" @default.
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