Some Examples in the Realization of Symmetry

TL;DR

This paper explores unusual realizations of symmetries in quantum mechanics, including confinement mechanisms, symmetry obstructions, and novel quantum statistics, with implications for condensed matter and supergravity theories.

Contribution

It introduces new phenomena related to symmetry realization in quantum systems, especially involving non-abelian structures and their physical implications.

Findings

Charge-flux frustration leads to confinement in coupled Chern-Simons models.

Non-abelian flux causes symmetry obstructions in 2+1D supergravity.

Potential for new quantum statistics, including non-abelian and projective types.

Abstract

I briefly discuss three phenomena arising in recent work where the realization of symmetries in quantum mechanics is unusual. The first of these is, I believe, the very simplest realization of non-trivial confinement by a mechanism of charge-flux frustration. It arises in models having several coupled abelian Chern-Simons gauge symmetries, which closely resemble effective theories used for the quantum Hall effect. The second is symmetry obstruction by non-abelian flux, which has implications for 2+1 dimensional supergravity. Third is the possibility of new varieties of quantum statistics: non-abelian and projective.