Goldstone modes of the girardello porratizaffaroni

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Unformatted text preview: oni, 2003). 1004 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . VI. CONCLUSIONS AND OUTLOOK We discussed the key mechanism by which higher-spin gravity evades the no-go theorems and, in particular, how the equivalence principle is reconciled with higher-spin gauge symmetry. Starting in flat spacetime, massless higher-spin particles cannot be reconciled with the equivalence principle. Nevertheless, the Weinberg-Witten theorem does not rule out higher-derivative energy-momentum tensors made out of higher-spin gauge fields. Hence massless higher-spin particles may couple nonminimally to a massless spin-two particle. However, in such a case the low-energy Weinberg theorem rules out the self-coupled Einstein-Hilbert action and minimally coupled matter, in particular, with low spins (i.e., s ¼ 0, 1=2, and 1), in contradiction with observations. Going to AdS spacetime, the Lorentz minimal coupling reappears but only as a subleading term in a strongly coupled derivative expansion. In order to do weakly coupled calculations, even at the cubic level for higher-spin gravity, one thus needs a complete theory with the full derivative expansion under control. The simplest available candidate at the moment is Vasiliev’s theory. Remarkably, not only does it resolve all the difficulties reported in the no-go theorems, but actually it also seems to be the simplest unbroken higher-spin gravity in the sense that it corresponds, via AdS/CFT, to a free conformal field theory with only scalar and/or fermion fields, albeit in large number. Two major open problems that need to be considered are as follows:  Can the Fronsdal program be pursued until quartic vertices? It is not totally excluded that the answer be ‘‘no’’ under the requirement of perturbative locality. Moreover, scattering amplitudes in AdS can be defined without using an action principle, and the recent checks of the AdS/ CFT correspondence in the context of higher-spin gravity at the cubic level were done by using the unfolded formalism in the bulk theory.  Does the dimensionless coupling in higher-spin gravity become large at low energies in AdS? If the answer is ‘‘yes’’ then higher-spin gravity is a promising candidate for an effective quantum gravity theory. Drawing on our experience with QCD, since higher-spin gravity has been observed to be extremely soft at high energy, it is tempting to think that the coupling constant becomes weak in the ultraviolet and should grow in infrared, such that the dynamical higher-spin symmetry breaking, which is present already in the ultraviolet, gives rise to a finite mass gap allowing the identification of the low-energy and low-spin regime. ACKNOWLEDGMENTS We are grateful to S. Leclercq for collaborations on several works closely related to this paper. We thank K. Alkalaev, G. Barnich, A. Bengtsson, F. Buisseret, A. Campoleoni, N. Colombo, P. P. Cook, V. Didenko, J. Engquist, D. Franc...
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