Abstract.
In these notes we review the method to construct integrable deformations of the compactified c = 1 bosonic string theory by primary fields (momentum or winding modes), developed recently in collaboration with S. Alexandrov and V. Kazakov. The method is based on the formulation of the string theory as a matrix model. The flows generated by either momentum or winding modes (but not both) are integrable and satisfy the Toda lattice hierarchy.
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Based on the talks presented at the James H. Simons Workshop on Random Matrix Theory Stony Brook, February 20 - 23, 2002, and the International Conference on Theoretical Physics Paris, UNESCO, July 22-27, 2002
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Kostov, I.K. Integrable Flows in c = 1 String Theory. Ann. Henri Poincaré 4 (Suppl 2), 825–849 (2003). https://doi.org/10.1007/s00023-003-0965-3
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DOI: https://doi.org/10.1007/s00023-003-0965-3