Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories

Abstract

It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three dimensional Anti de-Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.

LaTeX, 17 pages, no figures. The main text has been improved. A typo in the equations has been corrected, no qualitative change in the results. More examples have been discussed. More details on the physical interpretation have been added. Accepted for publication of Physical Review D

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