6-10 March 2017
Mainz Institute for Theoretical Physics, Johannes Gutenberg University
Europe/Berlin timezone

Hopf algebra gauge theories on embedded graphs

8 Mar 2017, 09:00
1h 30m
02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

02.430

Mainz Institute for Theoretical Physics, Johannes Gutenberg University

Staudingerweg 9 / 2nd floor, 55128 Mainz

Speaker

Catherine Meusburger

Description

We explain how the concept of a lattice gauge theory with values in a group can be generalised to a gauge theory with values in a Hopf algebra on a graph embedded into a surface. We give an axiomatic description of Hopf algebra gauge theories and show that they include the quantum algebra of observables obtained by the combinatorial quantisation of Chern-Simons theory as an example. We relate Hopf algebra gauge theories to lattice models from condensed matter physics. More specifically, we show that Kitaev's lattice model for a finite-dimensional semisimple Hopf algebra H is equivalent to a Hopf algebra gauge theory for its Drinfeld double D(H).

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