Gravitational Higgs Mechanism and Massive Gravity

TL;DR

This paper explores a gravitational Higgs mechanism where all but time-like diffeomorphisms are spontaneously broken, leading to a stable, massive graviton in dimensions up to 10, with a special focus on the critical dimension D=10.

Contribution

It demonstrates a classical realization of massive gravity with broken spatial diffeomorphisms and unbroken time-like diffeomorphism, highlighting stability and unitarity in specific dimensions.

Findings

Stable background for D <= 10 with no non-unitary modes

Mass squared of graviton positive for D < 10, zero at D=10

Tachyonic modes appear for D > 10

Abstract

In arXiv:hep-th/0011245, in the context of domain wall backgrounds, it was shown that spontaneous breaking of diffeomorphism invariance results in gravitational Higgs mechanism. Recently in arXiv:0708.3184 't Hooft discussed gravitational Higgs mechanism in the context of obtaining massive gravity directly in four dimensions, and pointed out some subtleties with unitarity. We attribute these subtleties to breaking time-like diffeomorphisms, and discuss gravitational Higgs mechanism with all but time-like diffeomorphisms spontaneously broken. The resulting background is no longer flat but exhibits expansion, which is linear in time. For space-time dimensions D <= 10 the background is stable and has no non-unitary propagating modes. The absence of non-unitary modes is due to the unbroken time-like diffeomorphism invariance. The physical states correspond to those of a massive graviton. The effective mass squared of the graviton is positive for D < 10, and vanishes for D = 10. For D > 10 the graviton modes become effectively tachyonic. The special value of D=10, which coincides with the critical dimension of superstring theory, arises in our setup completely classically.