Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exotic smooth R^4, geometry of string backgrounds and quantum D-branes   In this paper we make a first step toward determining 4-dimensional data from
higher dimensional superstring theory and considering these as underlying
structures for the theory. First, we explore connections of exotic smoothings
of R^4 and certain configurations of NS and D-branes, both classical and
(generalized) quantum using C* algebras. Effects of some small exotic R^4's,
when localized on S^3, correspond to stringy geometries of B-fields on S^3.
Exotic smoothness of R^4 acts as a non-vanishing B-field on S^3. The dynamics
of D-branes in SU(2) WZW model at finite k indicates the exoticness of ambient
R^4. Next, based on the relation of exotic smooth R^4 with integral levels of
SU(2) WZW model we show the correspondence between exotic smoothness on
4-space, transversal to the world volume of NS5 branes, and the number of these
NS5 branes. Relation with the calculations in holographically dual
6-dimensional little string theory is discussed. Generalized quantum D-branes
in the noncommutative C* algebras corresponding to the codimension-1 foliations
of S^3 are considered and these determine the KK invariants of exotic smooth
R_h^4 for the case of non-integral $[h]\in H^3(S^3,R)$. Moreover, exotic smooth
R^4's embedded in some exotic R^4 as open submanifolds, are shown to correspond
to generalized quantum D-branes in the noncommutative C* algebra of the
foliation. Finally, we show how exotic smoothness of R^4 is correlated with D6
brane charges in IIA string theory. In the last section we construct wild
embeddings of spheres and relate them to D-brane charges as well to KK theory.
We conjecture that a quantum D-brane is wild embedding. Then we construct an
action for a quantum D-brane and show that the classical limit (the usual
embedding) agrees with the Born-Infeld action.

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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg