Of cartan of the differential equations under

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Unformatted text preview: consideration. Thus, in order to avoid pathologies, it makes sense to follow a specific gauge principle,13 which for high spins is nothing but a refined version (e.g., the Noether procedure) of the naive application of the minimal coupling prescription, as is the main topic of this review. In particular, the electromagnetic interactions exhibit pathologies (such as seemingly superluminal propagation) in Minkowski spacetime already for massive spin- 3 fields [see 2 Velo and Zwanziger (1969) and Velo (1972) and a more recent analysis by Porrati and Rahman (2008, 2009) which contain a list of other relevant references on the issue] that are 13 Weinberg emphasized a related point, while mentioning the Velo-Zwanziger paper and other related works (cf. references therein), in his book (Weinberg, 1995), p. 244: ‘‘The problems reported with higher spin have been encountered only for higherspin particles that have been arbitrarily assumed to have only very simple interactions with external fields. No one has shown that the problems persist for arbitrary interactions. (. . .) There are good reasons to believe that the problems with higher spin disappear if the interaction with external fields is sufficiently complicated.’’ One may reinterpret this by stating that consistency requires less simplistic interactions, namely, those governed by gauge invariance. Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . therefore not specific to higher spins and hence deserve a separate discussion. Indeed, the interactions between spin- 3 2 and electromagnetic fields in gauged supergravities are well known to avoid the Velo-Zwanziger problems. In the case of spin-one self-interactions, a simple model to keep in mind is the Born-Infeld Lagrangian, whose expansion around a nontrivial electromagnetic background gives a linearized theory with causal structure governed by the Boillat metric whose light cone lies within that of the undeformed flat-space metric; see the discussion and references in Gibbons and Herdeiro (2001). In order to think of a model containing spins greater than 1 and with higher-derivative corrections that have been added following a gauge principle, one can immediately go to string theory, where the Born-Infeld theory is subsumed into open string theory. Open strings propagating in electromagnetic backgrounds (Argyres and Nappi, 1990) contain massive spin-s states with s ! 3 whose kinetic terms contain 2s À 2 2 derivatives. The actual physical problem is how to count degrees of freedom in the presence of extended spacetime gauge symmetries and the higher-derivative interactions that follow therefrom. In order to avoid nonintegrabilities in a systematic fashion, a natural resolution is to abandon the standard perturbative approach (formulating interactions in expansions around ordinary lower-spin backgrounds) in favor of the unfolded approach (Vasiliev, 1988, 1989, 1990, 1994) whic...
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This document was uploaded on 09/28/2013.

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