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数学大讲堂

Discrete fluxes in gauge theory and their duality

Abstract:
We explore the notion of discrete electric and magnetic fluxes introduced by ’t Hooft in the late 1970s. After explaining their physics origin, we consider the mathematical description. We start from several interpretations of characteristic classes of principal bundles over four manifolds. We then show that a global discrete symmetry in gauge theory when the centre of the gauge group non-trivial actually changes the topological type of the bundles. This leads to the breaking of discrete symmetry and the concept of rectified discrete electric and magnetic fluxes. We study their duality when the gauge  group is exchanged by its Langlands dual.