Dispersionless Toda hierarchy and two-dimensional string theory
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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.
KeywordsNeural Network Correlation Function Complex System Nonlinear Dynamics Quantum Computing
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- 1.Ghoshal, D., Mukhi, S.: Topological Landau-Ginzburg model of two-dimensional string theory. TIFR/TH/9362, hep-th/9312189, December, 1993Google Scholar
- 2.Hanany, A., Oz, Y., Plesser, M.R.: Topological Landau-Ginzburg formulation and integrable structure of 2d string theory. IASSNS-HEP-94/1, hep-th/9401030, January, 1994Google Scholar
- 3.Danielsson, U.H.: Two-dimensional string theory, topological field theories and the deformed matrix model. CERN-TH.7155/94, hep-th/9401135, January, 1994Google Scholar
- 6.Losev, A.: Descendents constructed from matter field in topological Landau-Ginzburg theories to topological gravity. ITEP preprint, hep-th/9212090, January, 1993; Eguchi, T., Kanno, H., Yamada, Y., Yang, S.K.: Topological strings, flat coordinates and gravitational descendents. Phys. Lett.B305, 235–241 (1993)Google Scholar
- 7.Lian, B., Zuckerman, G.: New selection rules and physical states in 2D gravity. Phys. Lett.B254, 417–423 (1991); Mukherji, S., Mukhi, S., Sen, A.: Null vectors and extra states inc=1 string theory. Phys. LettB266, 337–344 (1991); Bouwknegt, P., McCarthy, J., Pilch, K.: BRST analysis of physical states for 2D gravity coupled toc≦1 matter. Commun. Math. Phys.145, 541–560 (1992)CrossRefGoogle Scholar
- 9.Dubrovin, B.A.: Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginzburg models. Commun. Math. Phys.145, 195–207 (1992)Google Scholar
- 13.Moore, G., Seiberg, N.: From loops to fields in 2d gravity. Int. J. Mod. Phys.A7, 2601–2634 (1992); Minic, D., Polchinski, J., Yang, Z.: Translation-invariant backgrounds in 1+1 dimensional string theory. Nucl. Phys.B369, 324–360 (1991); Avan, J., Jevicki, A.: Quantum integrability and exact eigenstates of the collective string field theory. Phys. Lett.B272, 17–24 (1991); Das, S.R., Dhar, A., Mandal, G., Wadia, S.R.: Gauge theory formulation of thec=1 matrix model: Symmetries and discrete states. Int. J. Mod. Phys.A7, 5165–5192 (1992)CrossRefGoogle Scholar
- 15.Kutasov, D., Martinec, E., Seiberg, N.: Ground rings and their modules in two-dimensional string theory. Phys. Lett.B276, 437–444 (1992); Klebanov, I.: Ward identities in two-dimensional string theory. Mod. Phys. Lett.A7, 723–732 (1992); Witten, E., Zwiebach, B.: Algebraic structures and differential geometry in 2d string theory. Nucl. Phys.B377, 55–112 (1992); Verlinde, E.: The master equation of 2D string theory. Nucl. Phys.B381, 141–157 (1992)CrossRefGoogle Scholar