Vertices are expressed in terms of a single one

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Unformatted text preview: lts seem to apply in Minkowski spacetime (Metsaev, 1991). When the spin is unbounded, higher-spin interactions are nonperturbatively nonlocal but perturbatively local, in the rough sense that the number of derivatives is controlled by the length scale. More precisely, at any finite order in the power expansion in ‘ the vertices are local, but if all terms are included, as usually required for consistency at the quartic level, then the number of derivatives is unbounded. Summarizing: Nonlocality: The number of derivatives is unbounded in any perturbatively local vertex including an infinite spectrum of massless particles with unbounded spin. The good news is that nonlocal theories do not automatically suffer from the higher-derivative problem. For nonlocal theories that are perturbatively local, the problem can be treated if the free theory is well behaved and if nonlocality is cured perturbatively [see Simon (1990) for a comprehensive review on this point]. (iv) Massless higher-spin vertices are controlled by the infrared scale Concretely, in quantum field theory computations where massless particles are involved, one makes use of infrared and ultraviolet cutoffs where ‘IR and ‘UV denote the corresponding length scales (‘UV ( ‘IR ). By definition of the cutoff prescription, the typical wavelength of physical excitations ‘ (roughly, the ‘‘size of the laboratory’’) must be such that ‘UV < ‘ < ‘IR . In low-spin physics, the ultraviolet scale is of the order of the Planck length ‘UV $ ‘p , interactions are controlled by that ultraviolet cutoff, and nonrenormalizable theories are weakly coupled in the low-energy regime ‘ ) ‘p . In higher-spin gauge theory, the situation is turned upside down: interactions are controlled by the infrared cutoff ‘IRðhigher spinÞ (e.g., the AdS radius) and, since they are higher derivative, the theory is strongly coupled in the high-energy regime ‘ ( ‘IRðhigher spinÞ . D. Higher-spin symmetry breakings While the transition from massless to massive higher-spin ¨ particles is well understood at the tree level via the Stuckelberg mechanism, the higher-spin symmetry breaking remains unknown at the interacting level. The qualitative scenario is Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . briefly discussed in Sec. IV.D.1 and, finally, a tentative summary of the possible scenarios is presented in Sec. IV.D.2. 1. Higher-spin gauge symmetries are broken at the infrared scale At energies of the order of the infrared cutoff for the higher-spin gauge theory, i.e., when ‘ $ ‘IRðhigher spinÞ , higher-spin particles cannot be treated as ‘‘massless’’ any more. Instead, they get a mass of the order of ‘À1higher spinÞ IRð and, consequently, the higher-spin gauge symmetries are broken. Therefore, the no-go theorems do not apply any more. Hence, low-spin physics can be recovered at energy lower than the infrared...
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This document was uploaded on 09/28/2013.

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