132 research outputs found
Poisson-Lie T-duality as a boundary phenomenon of Chern-Simons theory
We give a "holographic" explanation of Poisson-Lie T-duality in terms of
Chern-Simons theory (or, more generally, in terms of Courant sigma-models) with
appropriate boundary conditions.Comment: 17 pages (a mistake in the energy-momentum tensor on p.2 corrected
On Deformation Quantization of Poisson-Lie Groups and Moduli Spaces of Flat Connections
We give simple explicit formulas for deformation quantization of Poisson-Lie
groups and of similar Poisson manifolds which can be represented as moduli
spaces of flat connections on surfaces. The star products depend on a choice of
Drinfe\v{l}d associator and are obtained by applying certain monoidal functors
(fusion and reduction) to commutative algebras in Drinfe\v{l}d categories. From
a geometric point of view this construction can be understood as a quantization
of the quasi-Poisson structures on moduli spaces of flat connections.Comment: 11 page
- …