Gauge theory for spectral triples via the unbounded KK-product
Bram Mesland (University of Warwick)
Tuesday 5th February, 2013 16:00-17:00 Maths 203
Unbounded KK-cycles with connection can be viewed a fibrations of spectral triples. When a noncommutative spectral triple is fibered, via such a cycle, over a commutative base, a natural setting for gauge theory presents itself. By considering gauge trnasformations that are implemented by fibrewise unitaries in the KK-cycle, the fact that commutative algebras don not possess nontrivial inner automorphisms is conveniently accounted for. Moreover, the connection allows for the distinction between horizontal and vertical differential forms on the spectral triple at hand. We will discuss this formalism for the noncommutative torus, and in the topologically nontrivial setting of the noncommutative 3-sphere. This is joint work with Simon Brain (Trieste) and Walter van Suijlekom (Nijmegen).