8 research outputs found
Nonreductive WZW models and their CFTs
We study two-dimensional WZW models with target space a nonreductive Lie
group. Such models exist whenever the Lie group possesses a bi-invariant
metric. We show that such WZW models provide a lagrangian description of the
nonreductive (affine) Sugawara construction. We investigate the gauged WZW
models and we prove that gauging a diagonal subgroup results in a conformal
field theory which can be identified with a coset construction. A large class
of exact four-dimensional string backgrounds arise in this fashion. We then
study the topological conformal field theory resulting from the coset. We
identify the Kazama algebra extending the BRST algebra, and the BV algebra
structure in BRST cohomology which it induces.Comment: dvi.uu (34 pages
BRST Quantization of String Theory in AdS(3)
We study the BRST quantization of bosonic and NSR strings propagating in
AdS(3) x N backgrounds. The no-ghost theorem is proved using the
Frenkel-Garland-Zuckerman method. Regular and spectrally-flowed representations
of affine SL(2,R) appear on an equal footing. Possible generalizations to
related curved backgrounds are discussed.Comment: JHEP style, 23 pages; v2:minor changes and references added; v3:
typos corrected, version to appear in JHEP; v4: one reference adde
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