EXOTIC SMOOTH ℝ4 AND CERTAIN CONFIGURATIONS OF NS AND D BRANES IN STRING THEORY

Abstract

In this paper, 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 ℝ4, (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 ℝ4. 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 ℝ4. 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 ℝ4 is achieved.