Title: Spin 1/2 from Colour and a Little More

Abstract: The theta vacuum in QCD is the standard vacuum, twisted by the exponential of the Chern-Simons term. But what is the quantum operator U(g) for winding number 1? We construct U(g) in this talk. The Poincare’ generators commute with it only if they are augmented by a spin 1/2 representation of the Lorentz group coming from large gauge transformations. This result is analogous to the ‘spin-isospin ‘ mixing result due to Jackiw and Rebbi, and Hasenfratz and ’t Hooft and a similar result in fuzzy physics. (See ‘Lectures on Fuzzy and Fuzzy SUSY Physics’ by Balachandran, S. Kurkcuoglu and S.Vaidya, chapters 5.4.1, 8.4.1)

Hence states can drastically affect representations of observables. This fact is further shown by charged states dressed by infrared clouds. Following Mund, Rehren and Schroer(arXiv:2109.10342), we find that Lorentz invariance is spontaneously broken in these sectors. This result is extended to QCD where even the global QCD group is shown to be broken.

It is argued that the escort fields of Mund et al. are the Higgs fields for Lorentz and colour breaking. They are string-localised fields where the strings live in a union of de Sitter spaces. Their oscillations and those of the infrared clouds generate the Goldstone modes.

Talk – Video

Talk – Slides