Gravitational Higgs mechanism: the role of determinantal invariants

Abstract

The Higgs mechanism for gravity, as proposed by 't Hooft in arXiv: 0708.3184 [hep-th], can be augmented by including determinantal invariants. We analyze the effects of determinantal invariants in such a set up. We find that the part of the potential that depends on the determinantal invariants, if obtains a specific exponential form in terms of its argument, may not affect the graviton mass calculated.

Constraints on a gravitational Higgs mechanism

“…number of massive higher-spin particles. 11 Both of these examples contain infinite towers of massive particles with masses that are not parametrically separated. An obvious further question is whether there can be a weakly-coupled UV completion of massive gravity with a parametrically large gap between the mass of the graviton and the scale of new physics, or whether any UV extension exists using only a finite number of higher-spin particles.…”

“…In this appendix we collect various details and conventions used in our calculations. 11 For example, in open bosonic string theory without Chan-Paton factors, the massive spin-2 particle on the leading Regge trajectory has cubic interactions of the form 2-2-s with all of the even spin-s states on the leading trajectory with masses m 2 s = (s − 1)/α [58],…”

“…However, despite this intuition, we would like to know if there is a fully Poincaréinvariant gravitational Higgs mechanism. This question is an old one, and there are many previous proposals and studies, see for example [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In terms of the S-matrix, the question is whether there is a method of raising the UV strong coupling scale of an effective field theory of self-interacting massive spin-2 bosons while remaining weakly coupled.…”

Determinantal invariant gravity

“…Where R lin is the determinant of the linearized Ricci tensor. Using empty space condition for energy momentum tensor of matter, T µν = 0, the linearized solution [11,13] of equation (4) in the Minkowski background, expanding determinantal potential about r = 0, is obtained as…”

“…One can construct such a determinantal invariant with the same analogy in [10,11]. The ratio of determinant of the Ricci tensor and metric tensor [12] is…”