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.

arXiv comment15 pages, Based on the talk ,,Small exotic smooth R^4 and string theory given at the International Congress of Mathematicians, ICM2010, 19-28.08.2010, Hyderabad, India

References in corpus (10)

• D-branes in the WZW model
• Twisted K-theory and K-theory of bundle gerbes
• Noncommutative Geometry and Gauge Theory on Fuzzy Sphere
• Exotic Smoothness and Physics
• Localized Exotic Smoothness
• Generation of Source Terms in General Relativity by differential structures
• Exotic Differentiable Structures and General Relativity
• Note on DBI dynamics of Dbrane Near NS5-branes
• Exotic Smoothness and Quantum Gravity
• Knotting corks

Cited by in corpus (4)

• Topological quantum D-branes and wild embeddings from exotic smooth R^4
• Quantum D-branes and exotic smooth R^4
• Exotic smooth R^4 and quantum matter
• The modification of the energy spectrum of charged particles by exotic open 4-smoothness via superstring theory