Theta term in a bounded region

Details Theta term in a bounded region Theta term in a bounded region

2011-05-12

arxiv.org/abs/1105.2490v2

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, no figures. Minor changes, added references. To appear in Phys. Rev. D

Scientific paper

We analyse the physical implications of adding a topological density term $\theta Tr(F\wedge F)$ to a gauge theory in a bounded region. In particular, we calculate the Casimir effect on a spherical region and we show that the result is not periodic in $\theta$, contrary to what would be expected for a true topological density. The topological nature of the $\theta$-term can be restored if an additional boundary term required by the Atiyah-Patodi-Singer theorem is included. Then, the periodicity is trivially restored because the resulting Casimir energy is independent of $\theta$. The results of the present work suggest that the observable effects of the $\theta$-term could be very small even without assuming $\theta$ itself to be small.

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