Quantum D-branes and exotic smooth R^4
arXiv:1102.3274 · doi:10.1142/S0219887812500223
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 R^4'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 S^3 which are mainly connected to small exotic R^4. The tools of topological K-homology and K-theory as well KK-theory describe stable quantum branes in the C* algebras when naturally extended to algebras. In case of convolution algebras, small exotic smooth R^4's embedded in exotic R^4 correspond to a generalized quantum branes on the algebras. These results extend the correspondence between exotic R^4 and classical D and NS branes from our previous work.
16 pages, no figure, see arXiv/1101.3169 for Part 1 This is part 2 of the work based on the talk "Small exotic smooth and string theory" given at the International Congress of Mathematicians, ICM2010, 19-28.08.2010, Hyderabad, India
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