R. Mader | Searcharxiv

arXiv2011

Exotic R^4 and quantum field theory

Recent work on exotic smooth R^4's, i.e. topological R^4 with exotic differential structure, shows the connection of 4-exotics with the codimension-1 foliations of $S^{3}$, SU(2) WZW models and twisted K-theory $K_{H}(S^{3})$, $H\in H^{3}(S^{3},\mathbb{Z})$. These results made it possible to explicate some physical effects of exotic 4-smoothness. Here we present a relation between exotic smooth R^4 and operator algebras. The correspondence uses the leaf space of the codimension-1 foliation of S^3 inducing a von Neumann algebra $W(S^{3})$ as description. This algebra is a type III_1 factor lying at the heart of any observable algebra of QFT. By using the relation to factor II, we showed that the algebra $W(S^{3})$ can be interpreted as Drinfeld-Turaev deformation quantization of the space of flat SL(2,\mathbb{C}) connections (or holonomies). Thus, we obtain a natural relation to quantum field theory. Finally we discuss the appearance of concrete action functionals for fermions or gauge fields and its connection to quantum-field-theoretical models like the Tree QFT of Rivasseau.

hep-th↗

arXiv2011

On 4-dimensional Lorentz-structures, Dark energy and Exotic smoothness

Usually, the topology of a 4-manifolds $M$ is restricted to admit a global hyperbolic structure $\Sigma\times\mathbb{R}$. The result was obtained by using two conditions: existence of a Lorentz structure and causality (no time-like closed curves). In this paper we study the influence of the smoothness structure to show its independence of the two conditions. Then we obtain the possibility for a topology-change of the 3-manifold $\Sigma$ keeping fix its homology. We will study the example $S^{3}\times\mathbb{R}$ with an exotic differential structure more carefully to show some implications for cosmology. Especially we obtain an interpretation of the transition in topology as dark energy.

gr-qc↗