Quantum Kramers-Wannier Duality And Its Topology

Abstract

We show for any oriented surface, possibly with a boundary, how to generalize Kramers-Wannier duality to the world of quantum groups. The generalization is motivated by quantization of Poisson-Lie T-duality from the string theory. Cohomologies with quantum coefficients are defined for surfaces and their meaning is revealed. They are functorial with respect to some glueing operations and connected with q-invariants of 3-folds.

LaTex, 16 pages, 18 figures

References in corpus (1)

• Dual Non-Abelian Duality and the Drinfeld Double

Cited by in corpus (5)

• Topological Transition on the Conformal Manifold
• Topological dualities in the Ising model
• Poisson-Lie T-duality as a boundary phenomenon of Chern-Simons theory
• Higher abelian Dijkgraaf-Witten theory
• Topologically ordered time crystals