Gribov ambiguity in asymptotically AdS three-dimensional gravity

TL;DR

This paper investigates the zero modes of the Faddeev-Popov operator in three-dimensional AdS gravity, revealing that the AdS vacuum has infinitely many zero modes while the BTZ black hole does not, impacting the understanding of ground states.

Contribution

It demonstrates the existence of infinitely many zero modes in the AdS vacuum and their absence in the BTZ black hole, suggesting the zero mass BTZ black hole as a potential ground state in 3D gravity.

Findings

AdS vacuum produces infinitely many zero modes.

BTZ black hole does not generate zero modes.

Implications for ground state selection in 3D gravity.

Abstract

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.