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).

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