Geodesic
Landau–Ginzburg topological theories in the framework of GKM and equivalent hierarchies
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 2, pp. 280-292 
S. M. Kharchev; A. V. Marshakov; A. D. Mironov; A. Yu. Morozov. Landau–Ginzburg topological theories in the framework of GKM and equivalent hierarchies. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 2, pp. 280-292. http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a12/
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     author = {S. M. Kharchev and A. V. Marshakov and A. D. Mironov and A. Yu. Morozov},
     title = {Landau{\textendash}Ginzburg topological theories in the framework of {GKM} and equivalent hierarchies},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1993_95_2_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the deformations of “monomial solutions” to Generalized Kontsevich Model [1,2] and establish the relation between the flows generated by these deformations with those of $N=2$ Landau–Ginzburg topological theories. We prove that the partition function of a generic Generalized Kontsevich Model can be presented as a product of some “quasiclassical” factor and non-deformed partition function which depends only on the sum of Miwa transformed and flat times. This result is important for the restoration of explicit $p-q$ symmetry in the interpolation pattern between all the $(p,q)$-minimal string models with $c<1$ and for revealing its integrable structure in $p$-direction, determined by deformations of the potential. It also implies the way in which supersymmetric Landau–Ginzburg models are embedded into the general context of GKM. From the point of view of integrable theory these deformations present a particular case of what is called equivalent hierarchies.

[1] Kharchev S. et al., 275B, Phys. Lett., 1992 | DOI | MR

[2] Kharchev S. et al., Nucl. Phys., B380 (1992), 181 | DOI | MR

[3] Kharchev S. et al., Generalized Kontsevich model versus Toda hierarchy and discrete matrix models, preprint FIAN/TD/3-92, ITEP-M-3/92, february, 1992

[4] Lerche W., Vafa C., Warner N. P., Nucl. Phys., B324 (1989), 427 | DOI | MR

[5] Vafa C., Mod. Phys. Lett., A6 (1990), 337 | MR | Zbl

[6] Dijkgraaf R., Verlinde H., Verlinde E., Nucl. Phys., B352 (1991), 59 | DOI | MR

[7] Lossev A., Descendans constructed from matter fields and K.Saito higher residue pairing in Landau–Ginzburg theories coupled to topological gravity, preprint ITEP/TPI-MINN, may 1992 | MR

[8] Dijkgraaf R., Intersection theory, integrable hierarchies and topological field theory, preprint IASSNS-HEP-91/91, december 1991 | MR

[9] Marshakov A., On string field theory for $c\leqslant 1$, preprint FIAN/TD/08-92, june 1992 | Zbl

[10] Shiota T., Invent. Math., 83 (1986), 333 | DOI | MR | Zbl

[11] Krichever I., Comm. Math. Phys., 143 (1992), 415 | DOI | MR | Zbl

[12] Dubrovin B., Integrable systems in topological field theories, preprint Napoli Univ., december 1991 | MR

[13] Kharchev S. et al., Preprint FIAN/TD/13-92, 1992, to be published | MR

[14] Takasaki K., Takebe T., Sdiff(2) KP hierarchy, preprint RIMS-814, october 1991 | MR

[15] Takebe T., From general Zakharov–Shabat equations to the KP and the Toda lattice hierarchies, preprint RIMS-779, 1991 | MR

[16] Segal G., Wilson G., Publ. IHES, 61 (1985), 1 | DOI | MR

[17] Dijkgraaf R., Witten E., Nucl. Phys., B342 (1990), 486 | DOI | MR