Magnetic monopoles, squashed 3-spheres and gravitational instantons from exotic R^4

TL;DR

This paper links exotic smooth structures on R^4 to gravitational instantons, showing they can model magnetic monopoles and generate gauge boson masses, with implications for cosmology, particle physics, and condensed matter.

Contribution

It introduces a novel connection between exotic R^4 geometries and magnetic monopoles, providing a geometric framework for gauge symmetry breaking and mass generation.

Findings

Exotic R^4 geometries correspond to magnetic monopole configurations.

Exotic smoothness can induce gauge boson mass in pure Yang-Mills theory.

Results rely on quasi-modularity and foliation geometry in the limit.

Abstract

We show that, in some limit, gravitational instantons correspond to exotic smooth geometry on R^4. The geometry of this exotic R^4 represents magnetic monopoles of Polyakov-'t Hooft type and the BPS condition allows for the generation of the charges from the gravitational sources of exotic R^4. Higgs field is, as usual, present in the monopole configurations. We indicate some possible scenarios in cosmology, particle physics and condensed matter where pure SU(2) Yang-Mills theory on the exotic R^4 aquires non-zero mass for its gauge boson when the smoothness is changed to the standard R^4 and, then, it is described by Yang-Mills Higgs theory. The derivation of the results is based on the quasi-modularity of the expressions and the geometry of foliations in the limit.