EMERGENT CHIRAL-SYMMETRY - PARITY AND TIME-REVERSAL DOUBLES

There are numerous examples of approximately degenerate states of oppo site parity in molecular physics. Theory indicates that these doubles can occur in molecules that are reflection-asymmetric. Such parity dou bles occur in nuclear physics as well, among nuclei with odd A similar to 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 d etail, demonstrating their emergence as a surprisingly subtle conseque nce of the Born-Oppenheimer approximation, and emphasizing their bundl e-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-ene rgy'' degrees of freedom. This mechanism of restoring the symmetry nat urally leads to the aforementioned doublet structure. A novel byproduc t of this mechanism is the emergence of an approximate symmetry (corre sponding to the approximate degeneracy of the doubles) at low energies which is not evident in the full Hamiltonian. We also dis cuss the im plications of this mechanism for Skyrmion physics, monopoles, anomalie s and quantum gravity.