QUANTUM D-BRANES AND EXOTIC SMOOTH ℝ4

Abstract

In this paper, we present the idea that the formalism of string theory is connected with the dimension 4 in a new way, not covered by phenomenological or model-building approaches. The main connection is given by structures induced by small exotic smooth ℝ4's having intrinsic meaning for physics in dimension 4. We extend the notion of stable quantum D-branes in a separable noncommutative C⋆-algebras over convolution algebras corresponding to the codimension-1 foliations of S3 which are mainly connected to small exotic ℝ4. The tools of topological K-homology and K-theory as well as KK-theory describe stable quantum branes in the C⋆-algebras when naturally extended to algebras. In case of convolution algebras, small exotic smooth ℝ4's embedded in exotic ℝ4 correspond to a generalized quantum brane on the algebras. These results extend the correspondence between exotic ℝ4 and classical D and NS-branes from our previous work.