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We recall the emergence of a generalized gauge theory from a noncommutativeRiemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. Thisincludes a gauge group determined by the unitaries in the $*$-algebra $A$ andgauge fields arising from a so-called perturbation semigroup which isassociated to $A$. Our main new result is the interpretation of thisgeneralized gauge theory in terms of an upper semi-continuous $C^*$-bundle on a(Hausdorff) base space $X$. The gauge group acts by vertical automorphisms onthis $C^*$-bundle and can (under some mild conditions) be identified with thespace of continuous sections of a group bundle on $X$. This then allows for ageometrical description of the group of inner automorphisms of $A$.  We exemplify our construction by Yang-Mills theory and toric noncommutativemanifolds and show that they actually give rise to continuous $C^*$-bundles.Moreover, in these examples the corresponding inner automorphism groups can berealized as spaces of sections of group bundles that we explicitly determine.

Localizing gauge theories from noncommutative geometry