Alladi Ramakrishnan Hall

Spin 1/2 from Color and a Little More

A. P. Balachandran

Syracuse University

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. 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.