Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-02-27
J.Phys.A42:304021,2009
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, based on talk presented at the conference "Liouville field theory and statistical models", dedicated to the memory o
Scientific paper
10.1088/1751-8113/42/30/304021
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side for minimal string theories is completely formulated using simple manipulations with two polynomials, based on residue formulas from quasiclassical hierarchies. Explicit computations for particular models are performed and certain delicate issues of nontrivial relations among them are discussed. They concern the connections between different theories, obtained as expansions of basically the same stringy solution to dispersionless KP hierarchy in different backgrounds, characterized by nonvanishing background values of different times, being the simplest known example of change of the quantum numbers of physical observables, when moving to a different point in the moduli space of the theory.
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