Effective field theory for massive gravitons and gravity in theory space

By N. Arkani-Hamed, H. Georgi, M. Schwartz. 2002

759 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8a2640b51b262c16c84419bbd6482af690408e9e

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Citations in the corpus

Symmetron Cosmology (2011, background): “The first is the Vainshtein mechanism [34, 35, 36], which works when the scalars have derivative self-couplings which become important in the vicinity of massive sources such as the Earth.”
A clockwork theory (2016, background): “(For deconstructions of gravity in general scenarios see [41, 58] and for RS see [59].”
The Stueckelberg Field (2003, methodology): “(Watanabe et al., 1967) applied the Stueckelberg formalism to the Rarita–Schwinger (spin 3/2) field, whereas (Arkani-Hamed et al., 2003; Delbourgo and Salam, 1975; Luty et al., 2003) did it for the graviton (spin 2) field.”
Massive Gravity (2014, methodology): “Following the same Stückelberg trick non-linearly, one can ‘formally restore’ covariance by including four Stückelberg fields φ (a = 0, 1, 2, 3) and promoting the reference metric fμν , which may of may not be Minkowski, to a tensor fμν [446, 27], fμν −→ fμν = ∂μφ∂νφfab (2.”
Positive signs in massive gravity (2016, background): “Moreover, the high-energy behavior of the amplitude signals a parametrically low cutoff Λ5 [2], where for later convenience we define”
Degravitation of the cosmological constant and graviton width (2007, methodology): “As shown in [8, 9] the leading singularity is of order 1/m(4) and comes from the trilinear vertex.”
Zoology of condensed matter: framids, ordinary stuff, extra-ordinary stuff (2015, background): “5) act like a translation on the combination ∂μCν + ∂νCμ − ∂μ∂νφ, which readers familiar with the Stückelberg formulation of massive gravity will easily recognize [36].”
Galileon Cosmology (2009, background): “For instance, we could consider more general functions of π/MPl multiplying the Ricci scalar, or include corrections of the form (∂π)4/M4Pl, all of which would drop out in the limit MPl → ∞.”
Classical and Quantum Consistency of the DGP Model (2004, background): “A completely equivalent problem has been pointed out in the case of massive gravity [15].”
D‐branes in Standard Model building, gravity and cosmology (2003, background): “As it was argued in [328] massive gravity with a Fierz-Pauli term becomes strongly coupled at energies of the order E5 ∼ (m(4)g MP ).”