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 TMF, 1993, Volume 95, Number 2, Pages 280–292 (Mi tmf1467)

Landau–Ginzburg topological theories in the framework of GKM and equivalent hierarchies

S. M. Kharchev, A. V. Marshakov, A. D. Mironov, A. Yu. Morozov

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1993, 95:2, 571–582

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Citation: S. M. Kharchev, A. V. Marshakov, A. D. Mironov, A. Yu. Morozov, “Landau–Ginzburg topological theories in the framework of GKM and equivalent hierarchies”, TMF, 95:2 (1993), 280–292; Theoret. and Math. Phys., 95:2 (1993), 571–582

Citation in format AMSBIB
\Bibitem{KhaMarMir93} \by S.~M.~Kharchev, A.~V.~Marshakov, A.~D.~Mironov, A.~Yu.~Morozov \paper Landau--Ginzburg topological theories in the framework of GKM and equivalent hierarchies \jour TMF \yr 1993 \vol 95 \issue 2 \pages 280--292 \mathnet{http://mi.mathnet.ru/tmf1467} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1243255} \zmath{https://zbmath.org/?q=an:0847.53058} \transl \jour Theoret. and Math. Phys. \yr 1993 \vol 95 \issue 2 \pages 571--582 \crossref{https://doi.org/10.1007/BF01017143} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993ML10100012} 

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This publication is cited in the following articles:
1. Phys. Usp., 45:9 (2002), 915–954
2. A. D. Mironov, “Integrability in String/Field Theories and Hamiltonian Flows in the Space of Physical Systems”, Theoret. and Math. Phys., 135:3 (2003), 814–827
3. Morozov A., “Challenges of matrix models”, String Theory: From Gauge Interactions to Cosmology, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 208, 2006, 129–162
4. Alexandrov, A, “BGWM as second constituent of complex matrix model”, Journal of High Energy Physics, 2009, no. 12, 053
5. Morozov, A, “Exact 2-point function in Hermitian matrix model”, Journal of High Energy Physics, 2009, no. 12, 003
6. Morozov, A, “ON EQUIVALENCE OF TWO HURWITZ MATRIX MODELS”, Modern Physics Letters A, 24:33 (2009), 2659
7. Alexandrov, A, “PARTITION FUNCTIONS OF MATRIX MODELS AS THE FIRST SPECIAL FUNCTIONS OF STRING THEORY II. KONTSEVICH MODEL”, International Journal of Modern Physics A, 24:27 (2009), 4939
8. Mironov A., Morozov A., “Virasoro constraints for Kontsevich-Hurwitz partition function”, Journal of High Energy Physics, 2009, no. 2, 024
9. A. Yu. Morozov, “Unitary integrals and related matrix models”, Theoret. and Math. Phys., 162:1 (2010), 1–33
10. A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, “Complete set of cut-and-join operators in the Hurwitz–Kontsevich theory”, Theoret. and Math. Phys., 166:1 (2011), 1–22
11. O. S. Kruglinskaya, “Correlation functions and spectral curves in models of minimal gravity”, Theoret. and Math. Phys., 174:1 (2013), 78–85
12. Alexandrov A. Mironov A. Morozov A. Natanzon S., “On KP-Integrable Hurwitz Functions”, J. High Energy Phys., 2014, no. 11, 080
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