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allows a generalized perturbative formulation of ﬁeld theory
in the unbroken phase as well as in various generalized metric
phases and/or tensorial spacetimes (Vasiliev, 2001b, 2002;
Didenko and Vasiliev, 2004; Gelfond and Vasiliev, 2005).
To summarize this survey of no-go results, the genuine
obstacles to massless higher-spin interactions are the
Coleman-Mandula theorem, the low-energy Weinberg theorems, and the generalized Weinberg-Witten theorem.
III. POSSIBLE WAYS OUT In this section, we discuss the weaknesses of the
various hypotheses underlying the no-go theorems for interacting massless higher-spin particles in ﬂat spacetime.
Correspondingly, we present conceivable ways to surpass
the spin-two barrier. Of these openings, the principal escape
route is the Fradkin-Vasiliev mechanism in which the cosmological constant plays a dual role as infrared and ultraviolet regulators. This leads to Vasiliev’s fully nonlinear
equations, which set a new paradigm for a realm of exotic
higher-spin gravities that ﬁt naturally into the contexts of
weak-weak coupling holography and tensionless limits of
extended objects. This ‘‘main route’’ will be discussed in
more detail in Secs. V and VI.
A. Masslessness Implicitly, all of the aforementioned no-go theorems rely
on the hypothesis of a ﬂat spacetime background. Indeed, the
notion of massless particles is unequivocal only in theories
´
with Poincare-invariant vacua. In constantly curved nonﬂat
spacetimes, the mass operator (i.e., r2 ) is related to the
eigenvalues of the second Casimir operators of the spacetime
Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 993 isometry algebra and of the Lorentz algebra. It is only in ﬂat
spacetime, however, that the eigenvalues of the mass operator
are quantum numbers, which can be sent to zero leaving a
strictly massless theory without any intrinsic mass scale.
Thus, as far as theories in Minkowski spacetime are concerned, one may consider interpreting massless higher-spin
particles as limits of massive dittos. Such particles are consistent at low energies; on the experimental side, they are
de facto observed in hadronic physics as unstable resonances
albeit not as fundamental particles.14 However, this highenergy limit has its own problems: it is singular in general
as manifested by the van Dam–Veltman–Zakharov discontinuity in propagators of massive ﬁelds of spin greater than 3 .
2
Indeed, on the theoretical side, this fact is related to the
complicated nature of the tensionless limit of string theory
in ﬂat spacetime.
A clear physical picture of why the high-energy limit
cannot be used to ﬁnd massless higher-spin particles in ﬂat
spacetime is given by the example of higher-spin resonances
in quantum chromodynamics. Dimensionless quantities depend on the ratio E=m, where E and m are the energy and the
mass of the resonance, respectively. As E goes to inﬁnity with
m kept ﬁxed is equivalent to m tending to zero keeping E
constan...

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