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Pis'ma v Zh. Èksper. Teoret. Fiz., 2013, Volume 97, Issue 1, Pages 49–55 (Mi jetpl3327)  

This article is cited in 43 scientific papers (total in 43 papers)

METHODS OF THEORETICAL PHYSICS

Spectral duality in integrable systems from AGT conjecture

A. Mironovab, A. Morozovb, Y. Zenkevichcbd, A. Zotovb

a P. N. Lebedev Physical Institute, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow
c M. V. Lomonosov Moscow State University, Faculty of Physics
d Institute for Nuclear Research, Russian Academy of Sciences, Moscow

Abstract: We describe relationships between integrable systems with $N$ degrees of freedom arising from the AGT conjecture. Namely, we prove the equivalence (spectral duality) between the $N$-cite Heisenberg spin chain and a reduced gl$_N$ Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the AGT relation in the Nekrasov–Shatashvili (and further the Seiberg–Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg–Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter–Schrödinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the $2\times 2$ and $N\times N$ representations of the Toda chain and the famous AHH duality.

Funding Agency Grant Number
Federal Agency for Science and Innovations of Russian Federation 14.740.11.0347
14.740.11.0081
Ministry of Education and Science of the Russian Federation NSh-3349.2012.2
MK-1646.2011.1
Russian Foundation for Basic Research 10-02-00509
10-02-00499
12-01-00482
12-01-33071
11-02-90453
13-02-91002
12-02-92108
11-01-92612
The work was partially supported by the Federal Agency for Science and Innovations of Russian Federation under contracts 14.740.11.0347 (A.Z., Y.Z.) and 14.740.11.0081 (A. Mor, A. Mir), by NSh-3349.2012.2, by RFBR grants 10-02-00509 (A. Mir.), 10-02-00499 (A. Mor., Y.Z.), 12-01-00482 (A.Z.), 12-01-33071 mol_a_ved (A.Z., Y.Z.), and by joint grants 11- 02-90453-Ukr, 13-02-91002-ANF, 12-02-92108-Yaf-a, 11-01-92612-Royal Society. The work of A. Zotov was also supported in part by the Russian President fund MK-1646.2011.1.


DOI: https://doi.org/10.7868/S0370274X13010104

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English version:
Journal of Experimental and Theoretical Physics Letters, 2013, 97:1, 45–51

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Received: 03.12.2012
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Citation: A. Mironov, A. Morozov, Y. Zenkevich, A. Zotov, “Spectral duality in integrable systems from AGT conjecture”, Pis'ma v Zh. Èksper. Teoret. Fiz., 97:1 (2013), 49–55; JETP Letters, 97:1 (2013), 45–51

Citation in format AMSBIB
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\paper Spectral duality in integrable systems from AGT conjecture
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2013
\vol 97
\issue 1
\pages 49--55
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