Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems
نویسنده
چکیده
We work out finite-dimensional integral formulae for the scalar product of genus one states of the group G Chern-Simons theory with insertions of Wilson lines. Assuming convergence of the integrals, we show that unitarity of the elliptic KnizhnikZamolodchikov-Bernard connection with respect to the scalar product of CS states is closely related to the Bethe Ansatz for the commuting Hamiltonians building up the connection and quantizing the quadratic Hamiltonians of the elliptic Hitchin system.
منابع مشابه
Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory
This letter continues the program [17][12][20][21] aimed at analysis of the scalar product of states in the Chern-Simons theory. It treats the elliptic case with group SU2. The formal scalar product is expressed as a multiple finite dimensional integral which, if convergent for every state, provides the space of states with a Hilbert space structure. The convergence is checked for states with a...
متن کاملHolomorphic Bundles and Many-body Systems
We show that spin generalization of elliptic Calogero-Moser system, elliptic extension of Gaudin model and their cousins can be treated as a degenerations of Hitchin systems. Applications to the constructions of integrals of motion, angle-action variables and quantum systems are discussed. The constructions are motivated by the Conformal Field Theory, and their quantum counterpart can be treate...
متن کاملHitchin Systems at Low Genera
The paper gives a quick account of the simplest cases of the Hitchin integrable systems and of the Knizhnik-Zamolodchikov-Bernard connection at genus 0, 1 and 2. In particular, we construct the action-angle variables of the genus 2 Hitchin system with group SL2 by exploiting its relation to the classical Neumann integrable systems. 1 Hitchin systems As was realized by Hitchin in [16], a large f...
متن کاملDifference Equations and Highest Weight Modules of U Q [sl(n)]
The quantized version of a discrete Knizhnik-Zamolodchikov system is solved by an extension of the generalized Bethe Ansatz. The solutions are constructed to be of highest weight which means they fully reflect the internal quantum group symmetry.
متن کاملConnection Problems for Quantum Affine KZ Equations and Integrable Lattice Models
Cherednik attached to an affineHecke algebramodule a compatible systemof difference equations, called quantum affine Knizhnik–Zamolodchikov (KZ) equations. In the case of a principal series module, we construct a basis of power series solutions of the quantum affine KZ equations. Relating the bases for different asymptotic sectors gives rise to a Weyl group cocycle, which we compute explicitly ...
متن کامل