Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-12-15
Phys.Rev.D83:064023,2011
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, no figures. V2: Reference added
Scientific paper
10.1103/PhysRevD.83.064023
In this paper the zero modes of the de Donder gauge Faddeev-Popov operator for three dimensional gravity with negative cosmological constant are analyzed. It is found that the three dimensional AdS vacuum produces (infinitely many) normalizable, smooth zero modes of the Faddeev-Popov operator. On the other hand, it is found that the BTZ black hole (including the zero mass black hole) does not generate zero modes. This differs from the usual Gribov problem in QCD where close to the maximally symmetric vacuum, the Faddeev-Popov determinant is positive definite while "far enough" from the vacuum it can vanish. This suggests that the zero mass BTZ black hole could be a suitable ground state of three dimensional gravity with negative cosmological constant. Due to the kinematic origin of this result, it also applies for other covariant gravity theories in three dimensions with AdS_3 as maximally symmetric solution, such as new massive gravity and topologically massive gravity. The relevance of these results for SUSY breaking is pointed out.
Anabalon Andres
Canfora Fabrizio
Giacomini Alex
Oliva Julio
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