1 research outputs found
Higgs Bundles, Gauge Theories and Quantum Groups
The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger
equation in the equivariant integration over the moduli space of Higgs bundles
is revisited. We argue that the wave functions of the corresponding
two-dimensional topological U(N) gauge theory reproduce quantum wave functions
of the Nonlinear Schr\"{o}dinger equation in the -particle sector. This
implies the full equivalence between the above gauge theory and the
-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger
equation. This also implies the explicit correspondence between the gauge
theory and the representation theory of degenerate double affine Hecke algebra.
We propose similar construction based on the gauged WZW model leading to
the representation theory of the double affine Hecke algebra. The relation with
the Nahm transform and the geometric Langlands correspondence is briefly
discussed.Comment: 48 pages, typos corrected, one reference adde