Exotic smooth R^4 and quantum matter

TL;DR

This paper explores how superstring theory and exotic smooth structures on 4-manifolds can model quantum gravity effects in four-dimensional spacetime, using advanced string techniques like CFT and WZW models.

Contribution

It introduces a novel approach linking exotic smoothness on  to superstring backgrounds, providing new mathematical tools for quantum gravity in 4D.

Findings

Exotic -structures can be described using superstring techniques.

Magnetic fields and gravitational effects are modeled via CFT and WZW models.

The framework offers a new perspective on quantum gravity in four dimensions.

Abstract

We follow the point of view that superstring theory, as the theory of quantum gravity in the number of spacetime dimensions bigger than 4, serves as mathematics for both, 4 dimensional QG and exotic smoothness on open 4-manifolds. Extra-dimensions, supersymmetry or some other string techniques, belong to the mathematical toolkit suitable for the above purposes. Physics in dimension 4 is reached via exotic 4-geometries on $\mathbb{R}^4$. In the paper we discuss the techniques of exact superstring backgrounds, CFT and $SU(2)_k$ WZW models, as suitable for the description of effects assigned to the magnetic field and its gravitational backreactions on exotic Euklidean $\mathbb{R}^4$ which is the underlying smoothness for the 4-dimensional spacetime.