Rajan 2003 for the scalar eld contributions one

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Unformatted text preview: te derivative tail in the standard field equations already at first order in the weak-field expansion (Sezgin and Sundell, 2002a). This leads to tree-level amplitudes depending on the following two dimensionless scales: (i) the weak-field expansion coupling g ¼ ð‘p ÞðDÀ2Þ=2 that can always be taken to obey g ( 1; and (ii) the derivative-expansion coupling ð‘ÞÀnþ2 where ‘ is the characteristic wavelength. Thus the tails are strongly coupled around solutions that are close to the AdSD solution since here ‘ ( 1. C. Main lessons The first important lesson which one can draw from the previous discussions is that, contrary to widespread prejudices, many doors are left open for massless higher-spin particles. The second important lesson is that interactions for higher-spin gauge fields exist but are rather exotic. Some of their properties clash with standard lores inherited from lowspin physics, and indeed, there is no fundamental reason to expect that higher-spin fields must behave as their low-spin companions. Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 997 Some model-independent features of non-Abelian higherspin gauge theories seem to emerge from all known no-go theorems and yes-go examples. It appears that most of the exotic properties of higher-spin fields can roughly be explained by mere dimensional arguments. As done in the previous section, we introduce a parameter ‘ with the dimension of a length and rescale all objects in order to work with dimensionless Lagrangian L and fields ’. The action takes R the form S ¼ ‘ÀD dD xLð’; ‘@’; ‘2 @2 ’; . . .Þ where each derivative is always multiplied by a factor of ‘. The Lagrangian counterpart of Feynman rules in S-matrix arguments is the weak-field expansion, i.e., the fields ’ are perturbations around some background for which the higher-spin Lagrangian L (if any) admits a usual perturbative power expansion in terms of these fields ’. Around a stable vacuum solution, this expansion starts with a quadratic kinetic term Lð0Þ with at most two derivatives and it goes on with vertices of various homogeneity degrees in ’: a cubic vertex Lð1Þ , a quartic vertex Lð2Þ , etc. In the following we present four general facts (of which there is no proof in full generality but no counterexample has ever been found) that seem to capture universal properties of any massless higher-spin vertex. (i) Higher-spin vertices are local order by order in some length scale A function of the field and its derivatives (treated as independent variables) is said to be local if it depends only on a finite number of derivatives @’; @2 ’; . . . :; @k ’ (for some fixed integer k) and, moreover, if it depends only polynomially on these derivatives. In the Lagrangian framework, the strong form of locality is the condition that the Lagrangian L must be a local function of the field ’, i.e., the total number of derivatives is bounded from above (so, in our...
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