RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
Main page
About this project
Software
Classifications
Links
Terms of Use

Search papers
Search references

RSS
Current issues
Archive issues
What is RSS






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


J. Math. Phys., 2013, Volume 54, Issue 2, 22306 (Mi jmp8)  

Seiberg–Witten equations and non-commutative spectral curves in Liouville theory

L. Chekhovab, B. Eynardc, S. Ribaultcd

a School of Mathematics, Loughborough University, LE11 3TU Leicestershire, United Kingdom
b Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 Russia
c Institut de Physique Théorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette, France
d Laboratoire Charles Coulomb UMR 5221 CNRS-UM2, Université Montpellier 2, Place Eugène Bataillon, F-34095 Montpellier Cedex 5, France

Abstract: We propose that there exist generalized Seiberg–Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the energy-momentum tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov, and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00440-a
11-01-12037-ofi-m
11-02-90453-Ukr-f-a
Ministry of Education and Science of the Russian Federation NSh-4612.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
L. Chekhov is grateful to the Russian Foundation for Basic Research for support (Grant Nos. 11-01-00440-a, 11-01-12037-ofi-m-2011, and 11-02-90453-Ukr-f-a), to the Grant for Supporting Leading Scientific Schools NSh-4612.2012.1, and to the Program Mathematical Methods of Nonlinear Dynamics.


DOI: https://doi.org/10.1063/1.4792241


Bibliographic databases:

Document Type: Article

Language: English

Linking options:
  • http://mi.mathnet.ru/eng/jmp8

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:25

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019