Eld theory essentially since the boundary currents

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Unformatted text preview: ds. Thinking of free conformal scalar fields, the case of two dimensions is very special, in that the stress tensor forms a closed operator algebra (the Virasoro algebra). Indeed, already in three dimensions one encounters the full higher-spin current algebra as one expands the operator product between two stress tensor generators (including a scalar current rather than a central term). Thus, in the case of four-dimensional theories of quantum gravity, it seems that the simplest, most natural procedure would be to start from Vasiliev-like higher-spin gravities and then seek symmetry breaking mechanisms that correspond to breaking the higher-spin currents, followed by taking limits in which these decouple from operator product expansions. In fact, by putting more emphasis on the AdS/CFT correspondence, one provides further arguments (Girardello, Porrati, and Zaffaroni, 2003) as to why higher-spin gravity is a natural framework for seeking ultraviolet completions of general relativity. Ordinary general relativity together with various matter couplings (and without exotic vertices) may then appear at low energies as the result of the dynamical higher-spin symmetry breaking mechanism induced by radiative corrections proposed by Girardello, Porrati, and Zaffaroni (2003), provided that the induced noncritical mass gaps grow large at low energies. If so, higher-spin gravity may bridge general relativity and string theory, which might be needed ultimately in order to achieve nonperturbative unitarity. 24 Note that recently, in the AdS3 =CFT2 framework based on the bulk theories provided by Blencowe (1989) and Prokushkin and Vasiliev (1999), many interesting works appeared; see, e.g., Henneaux and Rey (2010), Campoleoni et al. (2010), Campoleoni, Fredenhagen, and Pfenninger (2011), Castro, Lepage-Jutier, and Maloney (2011), Chang and Yin (2011), Gaberdiel and Gopakumar (2011), Gaberdiel, Gopakumar, Hartman, and Raju (2011), Gaberdiel, Gopakumar, and Saha (2011), Gaberdiel and Hartman (2011), Gaberdiel and Vollenweider (2011), Kraus and Perlmutter (2011), and references therein. Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . E. Emergence of extended objects We now comment on the similarities and dissimilarities between higher-spin gravity, with its double perturbative expansion in terms of the dimensionless coupling g and the cosmological constant Ã, and string theory, with its double perturbative expansion in terms of the string coupling gs and the string tension Ts . On the one hand, both of these theories are genuine higher-derivative theories which implies that at fixed orders in g and gs , respectively, there are vertices with fields of sufficiently high spins involving arbitrarily large inverse powers of their massive parameters à and Ts , respectively. Thus, in order to understand their respective second quantizations (g and gs expansions), one must first obtain a sufficiently sophisti...
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