Approach vasiliev 1988 1989 1990 1994 which allows a

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Unformatted text preview: h 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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