Effective field theory for massive gravitons and gravity in theory space
Abstract
We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the CallanColemanWessZumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale M_{Pl} and a mass m_{g}, we find that there is a sensible effective field theory which is valid up to a highenergy cutoff Λ parametrically above m_{g}. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the FierzPauli form of the Lagrangian, the presence or absence of the van DamVeltmanZakharov discontinuity in general backgrounds, and the onset of nonlinear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all nonlinear corrections beyond the FierzPauli term are easily determined. The cutoff scales as Λ∼( m_{g}^{4}M_{Pl}) ^{1/5} for the FierzPauli theory, but can be raised to Λ∼( m_{g}^{2}M_{Pl}) ^{1/3} in certain nonlinear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.
 Publication:

Annals of Physics
 Pub Date:
 June 2003
 DOI:
 10.1016/S00034916(03)00068X
 arXiv:
 arXiv:hepth/0210184
 Bibcode:
 2003AnPhy.305...96A
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 22 pages, 7 diagrams