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 Callan–Coleman–Wess–Zumino 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 high-energy 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 Fierz–Pauli form of the Lagrangian, the presence or absence of the van Dam–Veltman–Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz–Pauli term are easily determined. The cutoff scales as Λ∼( m g 4 M Pl) 1/5 for the Fierz–Pauli theory, but can be raised to Λ∼( m g 2 M Pl) 1/3 in certain non-linear 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.
Highlights
It has recently been realized that non-gravitational extra dimensions can be generated dynamically from fundamentally four-dimensional gauge theories [1,2,3]
The construction of the Goldstone link fields for gravity is easiest to understand in analogy with the gauge theory case which we review in detail
After describing the general formalism, we study the case of a single graviton of mass mg in detail
Summary
It has recently been realized that non-gravitational extra dimensions can be generated dynamically from fundamentally four-dimensional gauge theories [1,2,3]. At low energies the link fields become non-linear sigma model Goldstone fields, which are eaten to yield a spectrum of massless and massive gauge bosons This spectrum may match the Kaluza-Klein tower of a compactified higher-dimensional theory and be phenomenologically indistinguishable from an extra dimension. We should emphasize that we are only interested in a low-energy description with sites and Goldstone link fields, which in a unitary gauge reproduces a finite spectrum of massless and massive gravitons This is not “deconstruction”, in the sense that we are not, for the moment, interested in a full UV completion of these theories. Right multiplication by an element of a gauge group in gauge theory translates to composition with a coordinate transformation in the gravity case This allows us to define links, with the quantum numbers of four-dimensional vectors. We will conclude this paper by discussing a number of other possible applications, as well as open problems and other directions for future research along these lines
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