Weakly coupled derivative expansion taking higher

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Unformatted text preview: ivative expansion. Taking higher-spin gravity seriously as a model for quantum gravity, the key issue is thus whether its loop corrections5, which are given in a weak-field expansion more reminiscent of the perturbative expansion of string theory than that of general relativity, may generate masses dynamically for the higher-spin fields? Remarkably, relying on arguments based on the anti–de Sitter/conformal field theory (AdS/CFT) correspondence (Girardello, Porrati, and Zaffaroni, 2003), the answer seems affirmative: the pattern of symmetry breaking is similar in spirit to that of ordinary quantum chromodynamics (QCD), with spin playing the role of color, the metric playing the role of an Abelian gauge field, and the Goldstone modes being two-particle states; in the leading order in perturbation theory, the spin-s field acquires mass for s > 2 while the spin-s À 1 Goldstone mode is the lightest bound state (in its parity sector) between the physical scalar and the massless spin-s À 2 particle. The crucial missing ingredient is a ‘‘confinement mechanism’’ that causes g to become large at low enough energies, thus creating a mass gap leading to a low-energy effective quantum gravity. 5 For related issues within the anti–de Sitter/conformal field theory (AdS/CFT) correspondence, see Klebanov and Polyakov (2002) and Sezgin and Sundell (2002b) and the recent advances due to Giombi and Yin (2009, 2010), which altogether point to the fact that fourdimensional higher-spin gravity should have a surprisingly simple ultraviolet behavior as a quantum field theory in anti–de Sitter spacetime, in the sense that its boundary dual is weakly coupled or even free, with a simple 1=N expansion. Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . Thus, the quantization of higher-spin gauge theories can lead to interesting models providing deepened insights into the interplay between quantum mechanics and geometry. These might be of relevance not only in the high-energy limit of quantum gravity and string theory, but also for providing new ideas in observational physics, such as, for example, in cosmology, where weakly coupled massless particles can serve as dark matter candidates. Finally, the development of the quantum theory of higher-spin fields may serve as a source of inspiration for seeking and testing new methods in quantum field theory, such as the application of deformation and geometric quantizations as well as topological models to dynamical systems with local degrees of freedom. Having provided all of these motivations for quantizing higher-spin gauge fields, it is perhaps surprising to discover that there is a drastic gap between Vasiliev’s on-shell approach to higher-spin gravity based on gauging a non-Abelian global-symmetry algebra and the Fronsdal program: the latter has so far been only partially completed, mainly at the cubic level [for a recent discussion on this i...
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This document was uploaded on 09/28/2013.

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