Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Pis'ma v Zh. Èksper. Teoret. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2013, Volume 97, Issue 1, Pages 49–55
DOI: https://doi.org/10.7868/S0370274X13010104
(Mi jetpl3327)
 

This article is cited in 63 scientific papers (total in 63 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
References:
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.
Received: 03.12.2012
English version:
Journal of Experimental and Theoretical Physics Letters, 2013, Volume 97, Issue 1, Pages 45–51
DOI: https://doi.org/10.1134/S0021364013010062
Bibliographic databases:
Document Type: Article
Language: English
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
\Bibitem{MirMorZen13}
\by A.~Mironov, A.~Morozov, Y.~Zenkevich, A.~Zotov
\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
\mathnet{http://mi.mathnet.ru/jetpl3327}
\crossref{https://doi.org/10.7868/S0370274X13010104}
\elib{https://elibrary.ru/item.asp?id=18791303}
\transl
\jour JETP Letters
\yr 2013
\vol 97
\issue 1
\pages 45--51
\crossref{https://doi.org/10.1134/S0021364013010062}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000316227600010}
\elib{https://elibrary.ru/item.asp?id=20435317}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874962637}
Linking options:
  • https://www.mathnet.ru/eng/jetpl3327
  • https://www.mathnet.ru/eng/jetpl/v97/i1/p49
  • This publication is cited in the following 63 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Письма в Журнал экспериментальной и теоретической физики Pis'ma v Zhurnal Иksperimental'noi i Teoreticheskoi Fiziki
    Statistics & downloads:
    Abstract page:569
    Full-text PDF :107
    References:74
    First page:5
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024