Spacetime more generally a key physical effect of

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Unformatted text preview: s the formation of cusps on spiky closed strings (Gubser, Klebanov, and Polyakov, 2002; Kruczenski, 2005) [for generalizations to membranes, see Sezgin and Sundell (2002b)]. At the cusps, solitonic bound states arise, carrying the quantum numbers of singletons (Engquist and Sundell, 2006). In the case of folded long strings, the resulting two-singleton closed-string states are massless symmetric tensors with large spin realized by Flato and Fronsdal (1978). In the extrapolation of this spectrum to small spins, which is tantamount to taking a tensionless limit, resides the anti–de Sitter graviton. Engquist and Sundell (2006) argued that in order for the tensionless limit to lead to a closed-string field theory with nontrivial interactions, it should be combined with sending the cosmological constant to infinity in a discretized model with fixed mass parameter. This yields first-quantized (0 þ 1)-dimensional models describing multisingleton states. These have continuum limits given by Wess-Zumino-Witten models with gauged W algebras (rather than Virasoro algebras) that can be realized in terms of symplectic bosons (Engquist and Sundell, 2006; Engquist, Sundell, and Tamassia, 2007) and real fermions. Engquist and Sundell (2006) furthermore argued that the coupling of these first-quantized models to higher-spin background fields requires their extension into Poisson sigma models in one higher dimension containing the original systems on their boundaries. In particular, in the case of a single singleton, that represents one string parton or membrane parton, these couplings are mediated via boundary and bulk vertex operators of a topological open string in the phase space of a singleton that is a particular example of the C model of Cattaneo and Felder (2000); the consistency of this first-quantized system with disk topology then requires Vasiliev’s equations. The resulting physical picture provides a concrete realization for an extended object that is already present in the FlatoFronsdal formula. This picture also matches well with the holographic framework: just as the weak-coupling stress tensor is deformed directly into the strong-coupling stress tensor on the CFT side, the graviton in higher-spin gravity is the continuation of that in closed-string theory. Moreover, the fact that topological C models underlie general associative algebras directly explains why Vasiliev’s equations are compatible with internal Chan-Paton factors. One is thus led to contemplate a more profound underlying framework for quantum field theory in general, based on Poisson sigma models and topological summation and that would naturally incorporate the gauge principle as well as radiative corrections; in the case of the topological open string, the additional zero modes arising from cutting holes in the disk can then provide a first-quantized realization of the massive Goldstone modes of the Girardello-PorratiZaffaroni mechanism (Girardello, Porrati, and Zaffar...
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This document was uploaded on 09/28/2013.

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