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**Unformatted text preview: **as well as
their relations with the Fradkin-Vasiliev vertices.
In summary, it may prove to be useful to confront the no-go
theorems with the yes-go examples already in the classical
Lagrangian framework, in order to emphasize the underlying
assumptions of the no-go theorems, even if it may require an
extra assumption about perturbative locality.
The paper is organized as follows: In Sec. II we begin by
spelling out the gauge principle in perturbative quantum
ﬁeld theory and its ‘‘standard’’ implementation within the
Fronsdal program for higher-spin gauge interactions. We then
survey the problematics of nontrivial scattering of massless
particles of spin greater than 2 in ﬂat spacetime, and
especially its direct conﬂict with the equivalence principle.
In Sec. III we list possible ways to evade these negative
results, both within and without the Fronsdal program. In
Sec. IV we review results where consistent higher-spin interactions have been found, in both ﬂat and (A)dS spacetimes.
Because of the fact that consistent interacting higher-spin
gravities indeed exist, at least for gauge algebras which are
inﬁnite-dimensional extensions of the (A)dS isometry algebra, an important question is related to the possible symmetry
breaking mechanisms that give a mass to the higher-spin
gauge ﬁelds. This is brieﬂy discussed in Sec. IV.D. After
reviewing why a classically complete theory is crucial in
higher-spin gravity, we lay out in Sec. V the salient features
of Vasiliev’s approach to a class of potentially viable models
of quantum gravity. We conclude in Sec. VI where we also
summarize some interesting open problems. Finally we devote two Appendixes to the review of some S-matrix no-go
theorems and to their reformulation in Lagrangian language.
More precisely, Appendix A focuses on Weinberg’s lowenergy theorem, while Appendix B concentrates on the
Weinberg-Witten theorem and its recent adaptation to gauge
theories by Porrati.
II. NO-GO THEOREMS IN FLAT SPACETIME This section presents various theorems7 that constrain
interactions between massless particles in ﬂat spacetime,
potentially ruling out nontrivial quantum ﬁeld theories with
gauge ﬁelds with spin s > 2 and vanishing cosmological
constant. The aim is to scrutinize some of their hypotheses
in order to exhibit a number of conceivable loopholes that
may lead to modiﬁed theories including massless higher spin,
as summarized in Sec. III. ance in perturbative quantum ﬁeld theory stems from the fact
that one and the same massless particle, thought of as a
representation of the spacetime isometry group, in general
admits (inﬁnitely) many implementations in terms of quantum ﬁelds sitting in different Lorentz tensors obeying respective free equations of motion. For more information, see,
e.g., Skvortsov (2008) and Boulanger, Iazeolla, and Sundell
(2009).
Only a subset of these ‘‘carriers,’’ namely, the primary
curvature tensors and all of their derivatives, actu...

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