Quantum D-branes and exotic smooth R4\mathbb{R}^4

Feb, 2011
18 pages
Published in:
  • Int.J.Geom.Meth.Mod.Phys. 09 (2012) 125022
e-Print:

Citations per year

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Abstract: (arXiv)
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.
Note:
  • 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 $\mathbb{R}^{4}$ and string theory' given at the International Congress of Mathematicians, ICM2010, 19-28.08.2010, Hyderabad, India
  • Exotic R**4
  • D-branes
  • C*-algebras and K-theory
  • D-brane
  • dimension: 4
  • algebra: C*
  • stability: quantum
  • membrane model
  • algebra: noncommutative
  • string model