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Exotic smooth \(\mathbb R^{4}\) and certain configurations of NS and D branes in string theory. (English) Zbl 1214.81184

Summary: We show that in some important cases, four-dimensional data can be extracted from superstring theory such that (i) the data are Euclidean four-geometries embedded in standard \(\mathbb R^{4}\), (ii) these data depend on NS and D brane charges of some string backgrounds, (iii) it is of potential relevance to four-dimensional physics, (iv) the compactification and stabilization techniques are not in use, but are rather replaced. We analyze certain configurations of NS and D-branes in the context of SU(2) WZW model and find the correlations with different exotic smoothings of \(\mathbb R^{4}\). First, the dynamics of D-branes in SU(2) WZW model at finite \(k\), i.e. the charges of the branes, refers to the exoticness of ambient \(\mathbb R^{4}\). Next, the correspondence between exotic smoothness on four-space, transversal to the world volume of NS5 branes in type IIA, and the number of these NS5 branes follows. Finally, the translation of ten-dimensional string backgrounds to Euclidean four-spaces embedded as open subsets in the standard \(\mathbb R^{4}\) is achieved.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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