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Toda Lattice Hierarchy and Generalized String Equations

Kanehisa Takasaki
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Abstract

String equations of the $p$-th generalized Kontsevich model and the compactified $c = 1$ string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to a hypothesis postulated in the literature, the generalized Kontsevich model at $p = -1$ does not coincide with the $c = 1$ string theory at self-dual radius. A broader family of solutions of the Toda lattice hierarchy including these models are constructed, and shown to satisfy generalized string equations. The status of a variety of $c \le 1$ string models is discussed in this new framework.

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Kanehisa Takasaki. 1995-07-10. Toda Lattice Hierarchy and Generalized String Equations. https://doi.org/10.1007/bf02101675

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