Dispersionless Toda hierarchy and two-dimensional string theory

Details Dispersionless Toda hierarchy and two-dimensional string theory Dispersionless Toda hierarchy and two-dimensional string theory

1994-03-31

arxiv.org/abs/hep-th/9403190v5

Commun.Math.Phys. 170 (1995) 101-116

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX 21 pages, KUCP-0067 (typos are corrected and a brief note is added)

Scientific paper

10.1007/BF02099441

The dispersionless Toda hierarchy turns out to lie in the heart of a recently proposed Landau-Ginzburg formulation of two-dimensional string theory at self-dual compactification radius. The dynamics of massless tachyons with discrete momenta is shown to be encoded into the structure of a special solution of this integrable hierarchy. This solution is obtained by solving a Riemann-Hilbert problem. Equivalence to the tachyon dynamics is proven by deriving recursion relations of tachyon correlation functions in the machinery of the dispersionless Toda hierarchy. Fundamental ingredients of the Landau-Ginzburg formulation, such as Landau-Ginzburg potentials and tachyon Landau-Ginzburg fields, are translated into the language of the Lax formalism. Furthermore, a wedge algebra is pointed out to exist behind the Riemann-Hilbert problem, and speculations on its possible role as generators of ``extra'' states and fields are presented.

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