2,284 research outputs found
Representation Theory of Chern Simons Observables
Recently we suggested a new quantum algebra, the moduli algebra, which was
conjectured to be a quantum algebra of observables of the Hamiltonian Chern
Simons theory. This algebra provides the quantization of the algebra of
functions on the moduli space of flat connections on a 2-dimensional surface.
In this paper we classify unitary representations of this new algebra and
identify the corresponding representation spaces with the spaces of conformal
blocks of the WZW model. The mapping class group of the surface is proved to
act on the moduli algebra by inner automorphisms. The generators of these
automorphisms are unitary elements of the moduli algebra. They are constructed
explicitly and proved to satisfy the relations of the (unique) central
extension of the mapping class group.Comment: 63 pages, late
D-branes in the WZW model
It is stated in the literature that D-branes in the WZW-model associated with
the gluing condition J = - \bar{J} along the boundary correspond to branes
filling out the whole group volume. We show instead that the end-points of open
strings are rather bound to stay on `integer' conjugacy classes. In the case of
SU(2) level k WZW model we obtain k-1 two dimensional Euclidean D-branes and
two D particles sitting at the points e and -e.Comment: 2 pages, LaTe
Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
The geometry of D-branes can be probed by open string scattering. If the
background carries a non-vanishing B-field, the world-volume becomes
non-commutative. Here we explore the quantization of world-volume geometries in
a curved background with non-zero Neveu-Schwarz 3-form field strength H = dB.
Using exact and generally applicable methods from boundary conformal field
theory, we study the example of open strings in the SU(2) Wess-Zumino-Witten
model, and establish a relation with fuzzy spheres or certain (non-associative)
deformations thereof. These findings could be of direct relevance for D-branes
in the presence of Neveu-Schwarz 5-branes; more importantly, they provide
insight into a completely new class of world-volume geometries.Comment: 19 pages, LaTeX, 1 figure; some explanations improved, references
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Brane Dynamics in Background Fluxes and Non-commutative Geometry
Branes in non-trivial backgrounds are expected to exhibit interesting
dynamical properties. We use the boundary conformal field theory approach to
study branes in a curved background with non-vanishing Neveu-Schwarz 3-form
field strength. For branes on an , the low-energy effective action is
computed to leading order in the string tension. It turns out to be a field
theory on a non-commutative `fuzzy 2-sphere' which consists of a Yang-Mills and
a Chern-Simons term. We find a certain set of classical solutions that have no
analogue for flat branes in Euclidean space. These solutions show, in
particular, how a spherical brane can arise as bound state from a stack of
D0-branes.Comment: 25 page
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