Spontaneous Lorentz and diffeomorphism violation, massive modes, and gravity
Abstract
Theories with spontaneous local Lorentz and diffeomorphism violation contain massless NambuGoldstone modes, which arise as field excitations in the minimum of the symmetrybreaking potential. If the shape of the potential also allows excitations above the minimum, then an alternative gravitational Higgs mechanism can occur in which massive modes involving the metric appear. The origin and basic properties of the massive modes are addressed in the general context involving an arbitrary tensor vacuum value. Special attention is given to the case of bumblebee models, which are gravitationally coupled vector theories with spontaneous local Lorentz and diffeomorphism violation. Mode expansions are presented in both local and spacetime frames, revealing the NambuGoldstone and massive modes via decomposition of the metric and bumblebee fields, and the associated symmetry properties and gauge fixing are discussed. The class of bumblebee models with kinetic terms of the Maxwell form is used as a focus for more detailed study. The nature of the associated conservation laws and the interpretation as a candidate alternative to EinsteinMaxwell theory are investigated. Explicit examples involving smooth and Lagrangemultiplier potentials are studied to illustrate features of the massive modes, including their origin, nature, dispersion laws, and effects on gravitational interactions. In the weak static limit, the massive mode and Lagrangemultiplier fields are found to modify the Newton and Coulomb potentials. The nature and implications of these modifications are examined.
 Publication:

Physical Review D
 Pub Date:
 March 2008
 DOI:
 10.1103/PhysRevD.77.065020
 arXiv:
 arXiv:0712.4119
 Bibcode:
 2008PhRvD..77f5020B
 Keywords:

 11.30.Cp;
 04.50.h;
 11.30.Er;
 12.60.i;
 Lorentz and Poincare invariance;
 Higherdimensional gravity and other theories of gravity;
 Charge conjugation parity time reversal and other discrete symmetries;
 Models beyond the standard model;
 High Energy Physics  Theory;
 Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 27 pages twocolumn REVTeX, accepted in Physical Review D