Expansion in its unbroken phase in powers of p in this

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Unformatted text preview: turbation theory of higher-spin gravity is more similar in spirit to that of open string theory. 22 Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 In other words, in flat spacetime there are severe no-go theorems forming a spin-two barrier that cannot be surpassed in the sense that massless particles of spins s > 2 cannot interact with massless particles of spins s 2 provided the lower-spin sector contains finite minimal spin-two couplings. Thus, if one wishes to proceed in seeking strictly massless higher-spin gauge theories (with à ¼ 0) then one is forced toward unnatural theories without any minimal spin-two couplings, whereas if one switches on a finite à then one is naturally led into the realms of higher-spin gravity. B. The need for a complete theory We now emphasize the need for a complete theory of higher-spin gravity already at the classical level, i.e., a consistent action principle, or alternatively, set of equations of motion, that contains a complete set of strongly coupled derivative corrections. To this end, we return to the Fradkin-Vasiliev cancellation mechanism within the Fronsdal program: in the presence of a nonvanishing cosmological constant Ã, the Lorentz minimal cubic coupling (two derivatives) for a spin-s field becomes embedded into the Fradkin-Vasiliev quasiminimal vertex terminating in the non-Abelian-type 2-s-s vertex (2s À 2 derivatives) that remains consistent in the à ! 0 limit (Boulanger, Leclercq, and Sundell, 2008); this ‘‘top vertex’’ is thus the seed from which the subleading powers in à are grown by imposing Abelian spin-s gauge invariance. The crux of the matter, however, is that the cubic piece of a complete action (consistent to all orders) may in principle contain additional nonminimal interactions with more derivatives that are strongly coupled in the à expansion. Applying dimensional analysis one arrives at the following problem: for à < 0 the on-shell amplitude (Witten diagram) with three external massless gauge bosons need not vanish, and since à now sets both the infrared cutoff (assuming the free theory to consist of standard tachyon-and-ghost free Fronsdal kinetic terms) and the mass scale for higherderivative vertices, the contributions to the amplitude from vertices with n derivatives grow similar to the nth power of a large dimensionless number. Thus, although the top (highestderivative) vertex dominates the terms with fewer derivatives inside the quasiminimal coupling (including the Lorentz minimal coupling), it will in its turn be washed out by any genuinely nonminimal interaction, whose couplings (overall normalization in units of Ã) must hence be determined in order to estimate the three-particle amplitude. Toward this end one may in principle work within a slightly refined Fronsdal program as follows: (i) fix a free Fronsdal action; (ii) parametrize all consistent cubic vertices including a nonlocal Born-Infeld tail, that is, a strongly coupled expansion in terms...
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