#### 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.

Done