Higgs Bundles, Gauge Theories and Quantum Groups
Citation:
Samson L. Shatashvili (with Anton Gerasimov), Higgs Bundles, Gauge Theories and Quantum Groups, Comm. Math. Phys., 277, 2008, 323 - 367Download Item:
0609024.pdf (Published (author's copy) - Peer Reviewed) 485.8Kb
Abstract:
The appearance of the Bethe Ansatz equation for the Nonlinea
r Schr ?odinger equa-
tion in the equivariant integration over the moduli space of
Higgs bundles is revisited.
We argue that the wave functions of the corresponding two-di
mensional topological
U
(
N
)
gauge theory reproduce quantum wave functions of the Nonlin
ear Schr ?odinger equation in
the
N
-particle sector. This implies the full equivalence betwee
n the above gauge theory
and the
N
-particle sub-sector of the quantum theory of Nonlinear Sch
r ?odinger equation.
This also implies the explicit correspondence between the g
auge theory and the represen-
tation theory of degenerate double affine Hecke algebra. We pr
opose similar construction
based on the
G/G
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
Author's Homepage:
http://people.tcd.ie/shatassDescription:
PUBLISHED
Author: SHATASHVILI, SAMSON
Type of material:
Journal ArticleSeries/Report no:
Comm. Math. Phys.;277;
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Bethe Ansatz equationLicences: