RevModPhys.84.987

Interfering with the basic assumptions of canonical

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Unformatted text preview: the basic assumptions of canonical second quantization that led up to the notion of free fields to begin with. Thus a satisfactory resolution seems certainly much more demanding than even that of quantizing ordinary general relativity (though the prolongation of the Einstein-Cartan reformulation of general relativity as a soldered Yang-Mills theory for the spacetime isometry algebra soon leads to infinite-dimensional algebras as well) which actually leaves 2 These constraints on massless particle scattering appear only in spacetimes of dimension D ! 4 to which we restrict our attention in this paper. Indeed, in dimension D 3 massless fields of helicity s ! 2 have no local propagating degrees of freedom. Pure massless higher-spin gravities in lower dimensions are of Chern-Simons type which do not share most of the exotic features of their higherdimensional cousins discussed here. 3 The precise link between, on the one hand, the Fradkin-Vasiliev cubic action and, on the other hand, the fully interacting Vasiliev equations, remains to be found. 4 We thus leave out many other interesting features of the Vasiliev system, such as its unfolded, or Cartan integrable, formulation, and the link between its first-quantization, deformed Wigner oscillators, singletons, and compositeness of massless particles in anti–de Sitter spacetime. Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 room for a naive optimism: the quantization of higher-spin gauge theories could lead to a radically new view on quantum field theory altogether, and, in particular, on the formidable spin-two barrier set up by the requirement of power-counting renormalizability. Indeed, at the classical level, there exist the aforementioned higher-spin gravities (Vasiliev, 1990, 1992, 1996, 2003; Sezgin and Sundell, 1998, 2001a,2001b, 2002a): these are special instances of interacting higher-spin gauge theories constituting what one may think of as the simplest possible higher-spin extensions of general relativity. Their minimal bosonic versions (in D ! 4 ordinary spacetime dimensions) consist of a propagating scalar, metric, and tower of massless fields of even spins, s ¼ 4; 6; . . . (these models can then be extended by various forms of ‘‘matter’’ and suitable higherspin counterparts, in a supersymmetric setup in case fermions are included). As mentioned, a key feature of higher-spin gravity is its double perturbative expansion: besides the expansion in numbers of fields, weighted by a dimensionless coupling g, there is a parallel albeit strongly coupled expansion in numbers of pairs of derivatives, weighted by a dimensionful parameter, the cosmological constant Ã, thus serving as both infrared and ultraviolet cutoff. Hence classical higherspin gravity prefers a nonvanishing cosmological constant, unlike string theory in flat spacetime which also has a double perturbative expansion but with a strictly massless sector accessible at low energies in a weakly coupled der...
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