Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-05-19
Commun.Math.Phys. 182 (1996) 185-220
Physics
High Energy Physics
High Energy Physics - Theory
54 pages, Plain TeX. Figure could be obtained from Kodama
Scientific paper
10.1007/BF02506390
Based on the dispersionless KP (dKP) theory, we give a comprehensive study of the topological Landau-Ginzburg (LG) theory characterized by a rational potential. Writing the dKP hierarchy in a general form, we find that the hierarchy naturally includes the dispersionless (continuous) limit of Toda hierarchy and its generalizations having finite number of primaries. Several flat solutions of the topological LG theory are obtained in this formulation, and are identified with those discussed by Dubrovin. We explicitly construct gravitational descendants for all the primary fields. Giving a residue formula for the 3-point functions of the fields, we show that these 3-point functions satisfy the topological recursion relation. The string equation is obtained as the generalized hodograph solutions of the dKP hierarchy, which show that all the gravitational effects to the constitutive equations (2-point functions) can be renormalized into the coupling constants in the small phase space.
Aoyama Shogo
Kodama Yuji
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