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**Unformatted text preview: **3)=987(23) 2. Dynamical symmetry breaking: Spin one
versus higher spin
V. Fully Interacting Example:
Vasiliev’s Higher-Spin Gravity
A. Examples of non-Abelian gauge theories
B. The need for a complete theory
C. Vasiliev’s equations
D. AdS/CFT correspondence: Vasiliev’s theory
from free conformal ﬁelds
E. Emergence of extended objects
VI. Conclusions and Outlook
Appendix A: Weinberg Low-energy Theorem:
S matrix and Lagrangian Dictionary
1. Emission of a massless particle: Lorentz
versus gauge invariances
2. Cubic vertices
Appendix B: Weinberg-Witten Theorem:
A Lagrangian Reformulation
1. Weinberg-Witten theorem
2. Reﬁnement of Weinberg-Witten theorem 987 Ó 2012 American Physical Society 988 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . interacting quantum ﬁeld theory.2 While this may seem to
call for radical measures, there exists a relatively conservative yet viable way out, namely, the dual usage of the
cosmological constant as critical mass (infrared cutoff)
and dimensionful coupling constant. This dual-purpose
treatment of the cosmological constant leads to a successful
exchange of what are leading and subleading terms in
minimal coupling that lifts the spell of the no-go theorems,
and, in particular, reconciles higher-spin gauge symmetry
with the equivalence principle, leading up to the FradkinVasiliev cubic action (Fradkin and Vasiliev, 1987b, 1987c;
Vasiliev, 2001a, 2011; Alkalaev and Vasiliev, 2003) and
Vasiliev’s fully nonlinear equations of motion3 (Vasiliev,
1990, 1992, 2003) [see, e.g., Vasiliev (2004a, 2004b) and
Bekaert and et al. (2005) for some reviews].
Since our aim is to outline main ideas and results, we
refrain from being technical and refer the interested reader to
the already existing literature whenever necessary. Moreover,
throughout the paper we mostly stick to the Fronsdal program
(Fronsdal, 1978), i.e., the standard perturbative off-shell
implementation of non-Abelian gauge deformations starting
from the Fronsdal actions in constantly curved backgrounds.
It is the gauge algebra (not necessarily an internal algebra)
that we require to become non-Abelian similar to the diffeomorphism algebra in Einstein gravity. As for Vasiliev’s
higher-spin gravity, presently the most far-reaching construction of a full higher-spin gauge theory, we restrict ourselves4
to a more brief address of how it presents a natural framework
for a string-theory-like double perturbative expansion.
Now, why are higher-spin gauge ﬁelds interesting?
Although massless ﬁelds of spin greater than 2 make perfect
sense at the free level, their quantum interactions pose a main
challenge to modern theoretical physics. In a nutshell, the
problematics can be summarized as follows: consistent nonAbelian higher-spin gauge symmetries induce local higherderivative generalizations of translations that seem to call for
a nontrivial bosonic extension of spacetime itself, thus interfering with...

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