Theta term in a bounded region

Abstract

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.

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

References in corpus (4)

• Tunable Casimir repulsion with three dimensional topological insulators
• Effect of finite temperature and uniaxial anisotropy on the Casimir effect with three-dimensional topological insulators
• Couplings between Chern-Simons gravities and 2p-branes
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• The Casimir effect in chiral media using path integral techniques
• Optical Properties of a θ-Vacuum
• Optical Properties Chern-Simons (3+1)D $\theta$-systems
• On the static Casimir effect with parity-breaking mirrors
• Casimir energy for a spherical boundary within the surface impedance approach: Obtaining negative values