Exotic smooth R^4 and certain configurations of NS and D branes in string theory

Abstract

In this paper we show that in some important cases 4-dimensional data can be extracted from superstring theory such that a) the data are 4 Euclidean geometries embedded in standard $\mathbb{R}^{4}$, b) these data depend on NS and D brane charges of some string backgrounds, c) it is of potential relevance to 4-dimensional physics, d) the compactification and stabilization techniques are not in use, but rather are 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 4-space, transversal to the world volume of NS5 branes in IIA type, and the number of these NS5 branes follows. Finally, the translation of 10 dimensional string backgrounds to 4 Euclidean spaces embedded as open subsets in the standard $\mathbb{R}^{4}$ is achieved.