Emergent Chiral Symmetry: Parity and Time Reversal Doubles

TL;DR

This paper explores the theoretical origins of parity and time reversal doublets across various physical systems, revealing their emergence as a subtle consequence of the Born-Oppenheimer approximation and topological effects, with broad implications.

Contribution

It demonstrates how classical symmetries broken at the quantum level can be restored through high-energy degrees of freedom, explaining the origin of parity and time reversal doublets.

Findings

Parity doubles occur in molecules, nuclei, and baryons.

Restoring symmetries involves high-energy degrees of freedom.

Emergence of approximate symmetries at low energies.

Abstract

There are numerous examples of approximately degenerate states of opposite parity in molecular physics. Theory indicates that these doubles can occur in molecules that are reflection-asymmetric. Such parity doubles occur in nuclear physics as well, among nuclei with odd A $\sim$ 219-229. We have also suggested elsewhere that such doubles occur in particle physics for baryons made up of `cbu' and `cbd' quarks. In this article, we discuss the theoretical foundations of these doubles in detail, demonstrating their emergence as a surprisingly subtle consequence of the Born-Oppenheimer approximation, and emphasizing their bundle-theoretic and topological underpinnings. Starting with certain ``low energy'' effective theories in which classical symmetries like parity and time reversal are anomalously broken on quantization, we show how these symmetries can be restored by judicious inclusion of ``high-energy'' degrees of freedom. This mechanism of restoring the symmetry naturally leads to the aforementioned doublet structure. A novel by-product of this mechanism is the emergence of an approximate symmetry (corresponding to the approximate degeneracy of the doubles) at low energies which is not evident in the full Hamiltonian. We also discuss the implications of this mechanism for Skyrmion physics, monopoles, anomalies and quantum gravity.