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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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