10 research outputs found
Donagi-Markman cubic for the generalised Hitchin system
Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS) is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We show that the Balduzzi\u2013Pantev formula holds on maximal rank symplectic leaves of the G-generalised Hitchin system
Dualities in integrable systems and N=2 theories
We discuss dualities of the integrable dynamics behind the exact solution to
the N=2 SUSY YM theory. It is shown that T duality in the string theory is
related to the separation of variables procedure in dynamical system. We argue
that there are analogues of S duality as well as 3d mirror symmetry in the
many-body systems of Hitchin type governing low-energy effective actions.Comment: 16 pages, Latex, Talk given at QFTHEP-99, Moscow, May 27-June
Solving loop equations by Hitchin systems via holography in large-N QCD_4
For (planar) closed self-avoiding loops we construct a "holographic" map from
the loop equations of large-N QCD_4 to an effective action defined over
infinite rank Hitchin bundles. The effective action is constructed densely
embedding Hitchin systems into the functional integral of a partially quenched
or twisted Eguchi-Kawai model, by means of the resolution of identity into the
gauge orbits of the microcanonical ensemble and by changing variables from the
moduli fields of Hitchin systems to the moduli of the corresponding holomorphic
de Rham local systems. The key point is that the contour integral that occurs
in the loop equations for the de Rham local systems can be reduced to the
computation of a residue in a certain regularization. The outcome is that, for
self-avoiding loops, the original loop equations are implied by the critical
equation of an effective action computed in terms of the localisation
determinant and of the Jacobian of the change of variables to the de Rham local
systems. We check, at lowest order in powers of the moduli fields, that the
localisation determinant reproduces exactly the first coefficient of the beta
function.Comment: 65 pages, late