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

Journal Article · Fri Feb 15 04:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4792241· OSTI ID:22162765

Chekhov, Leonid ^[1]; Eynard, Bertrand ^[2]; Ribault, Sylvain ^[2]

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1. Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 Russia and School of Mathematics, Loughborough University, LE11 3TU Leicestershire (United Kingdom)
2. Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France)

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.

• OSTI ID: 22162765
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 54; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
CALCULATION METHODS
CHIRAL SYMMETRY
CHIRALITY
COMMUTATION RELATIONS
CONFORMAL INVARIANCE
CORRELATION FUNCTIONS
ENERGY-MOMENTUM TENSOR
EQUATIONS
EXPANSION
PERTURBATION THEORY
QUANTUM FIELD THEORY
RESOLUTION
SPIN
WARD IDENTITY