Pure 4-geometry of quantum magnetic spin matter from Kondo effect

TL;DR

This paper links exotic smooth structures on R^4 to quantum magnetic spin matter, specifically the Kondo effect, proposing a geometric model where exotic smoothness encodes quantum interactions and bound states.

Contribution

It introduces a novel geometric framework connecting exotic smooth R^4 structures with quantum spin interactions and the Kondo effect, using topological and conformal field theory methods.

Findings

Exotic smooth R^4_k generates fermionic fields via Casson handles.

The number of Casson handles correlates with the number of Kondo channels.

Standard R^4 does not support quantum interactions in this model.

Abstract

We determine a smooth Euclidean 4-geometry on R^4 from quantum interacting spin matter like in the multichannel Kondo effect. The CFT description of both: the $k$-channel Kondo effect of spin magnetic impurities quantum interacting with spins of conducting electrons and exotic smooth R^4, by the level $k$ WZW model on SU(2), indicates the relation between smooth R^4's and the quantum matter. We propose a model which shows: exotic smooth R^4_k generates fermionic fields via the topological structure of Casson handles and when this handle is attached to some subspace A of R^4 these fermions represent electrons bounded by the magnetic impurity. Thus the Kondo bound state of $k$ conducting electrons with magnetic impurity of spin $s$ is created like in the low temperature Kondo effect. Then the quantum character of the interactions is encoded in 4-exoticness. The complexity as well the number of Casson handles correspond to the number of channels in the Kondo effect. When the smoothness structure is the standard one, no quantum interactions are carried on by standard R^4.