Toda Lattice Hierarchy and Generalized String Equations

Details Toda Lattice Hierarchy and Generalized String Equations Toda Lattice Hierarchy and Generalized String Equations

1995-06-13

arxiv.org/abs/hep-th/9506089v4

Commun.Math.Phys. 181 (1996) 131

Physics

High Energy Physics

High Energy Physics - Theory

35pages, LaTeX Errors are corrected in Eqs. (2.21), (2.36), (2.33), (3.3), (5.10), (6.1), sentences after (3.19) and theorem 5

Scientific paper

10.1007/BF02101675

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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