Quantum Hitchin Systems via beta-deformed Matrix Models
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Date
2011-05-17
Journal Title
Journal ISSN
Volume Title
Publisher
SISSA
Abstract
We study the quantization of Hitchin systems in terms of beta-deformations of
generalized matrix models related to conformal blocks of Liouville theory on
punctured Riemann surfaces. We show that in a suitable limit, corresponding to
the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce
the Hamiltonians of the quantum Hitchin system on the sphere and the torus with
marked points. The eigenvalues of these Hamiltonians are shown to be the
epsilon1-deformation of the chiral observables of the corresponding N=2 four
dimensional gauge theory. Moreover, we find the exact wave-functions in terms
of the matrix model representation of the conformal blocks with degenerate
field insertions.
Description
29 pages; v2. refs. added and typos corrected ; was issued as preprint SISSA n. 18/2011/EP-FM