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Unformatted text preview: olution to the problem of quantum
corrections to the cosmological constant. It is a remarkable
fact that the Ã3 theories of Sec. VIII exist and are ghost free,
and that they are found simply by tuning some coefﬁcients in
the generic graviton potential.
There are many interesting outstanding issues. One is the
nature of the Ã3 theory. Is there a symmetry or a topological
construction that explains the tunings of the coefﬁcients
necessary to achieve the Ã3 cutoff? Is there some construction free of prior geometry that would contain this theory? Is
there an extra-dimensional construction?
There are also many questions related to the quantum
properties of these theories. Apart from the order of magnitude estimates presented in this review and a few sporadic
calculations, the detailed quantum properties of this theory
and others remain relatively unexplored. The same goes for
nonperturbative quantum properties, such as how a massive
graviton would modify black hole thermodynamics, Hawking
radiation, or holography (Babak and Grishchuk, 2003;
Aharony, Clark, and Karch, 2006; Katz, Lewandowski, and
Schwartz, 2006; Kiritsis, 2006; Kiritsis and Niarchos, 2009;
Niarchos, 2009; Capela and Tinyakov, 2011).
The cutoff Ã3 is still rather low, however, so at best this
theory in its current perturbative expansion can provide only a
partial solution to the cosmological constant naturalness
problem. Finding more natural constructions of these theories
would go a long way toward solving the major issue, which is
that of UV completion; is it possible to ﬁnd a standard UV
completion for a massive graviton, analogous to what the
Higgs mechanism provides for a massive vector? Or is there
some incontrovertible obstruction that forces any UV Kurt Hinterbichler: Theoretical aspects of massive gravity completion to violate Lorentz invariance, locality, or some
other cherished property? If so, there may be a nonstandard
UV completion, or it could be that massive gravity really is
inconsistent, in the sense that there really is no way whatsoever to UV complete it. There has been work on holography
of massive gravitons in anti–de Sitter/conformal ﬁeld theory
(AdS/CFT) (Aharony, Clark, and Karch, 2006; Kiritsis, 2006;
Kiritsis and Niarchos, 2009; Niarchos, 2009), which provides
a UV completion for theories in AdS space containing massive gravity.
Even a partial UV completion, one that raises the cutoff to
MP , would be extremely important, as this is all that is
required to offer a solution to the cosmological constant
naturalness problem. One possibility is that the scale Ã3 ,
while indicating a breakdown in perturbation theory, does
not signal the activation of any new degrees of freedom, so
that the theory is already self-complete up to MP . Since there
are multiple parameters in the theory, it is likely that there is
some other expansion, such as a small m expansion, which
reorganizes the perturbation theory into one which yields
perturbative access to scales abov...
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