By tensoring together singletons flato and fronsdal

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Unformatted text preview: Dolan, 2006) which introduce the germ of an extended object23 as well as a precursor to AdS/CFT. In order to construct higher-spin extensions of fourdimensional gravity, the simplest higher-spin algebras of this type can be realized in terms of elementary noncommutative twistor variables. As a result the full field content of a special class of higher-spin gravity theories, that we refer to as the minimal bosonic models and their matter-coupled and supersymmetrized extensions, is packed up into finite sets of 23 The idea of treating algebras and their representations on a more equal footing, namely as various left-, right-, or two-sided modules arising inside the enveloping algebra and its tensor products, is in the spirit of modern algebra and deformation quantization. Indeed, further development of these thoughts lead to first-quantized systems linking higher-spin gravities to tensionless strings and branes (Engquist and Sundell, 2006). Rev. Mod. Phys., Vol. 84, No. 3, July–September 2012 1001 ‘‘master’’ fields living on the product of a commutative spacetime and a noncommutative twistor space. The feat of Vasiliev was then to realize that these master fields can be taken to obey remarkably simple-looking master equations built using exterior differential calculus on spacetime and twistor space, and star products on twistor space, reproducing the standard second-order equations in perturbation theory, in about the same way in which Einstein’s equations arise inside a set of on-shell superspace constraints via constraints on the torsion and Riemann two-forms. As a result, Vasiliev’s equations are diffeomorphic invariant, in the sense of unfolded dynamics, and perturbatively equivalent to a standard set of on-shell Fronsdal fields albeit with interactions given by a nonlocal double perturbative expansion resulting from the star products. Looking at the twistor-space structure one sees that it services two purposes. In naive double perturbation theory, the expansion in the twistor variables combined with star products simply generates the higher-spin tensor calculus that one may take to define the minimal bosonic models after which one can naively strip off all the twistor variables by Taylor expansion and make contact with the standard tensorial equations of motion after having eliminated infinite towers of auxiliary fields. A more careful look at these tensorial equations of motion reveals, however, Born-Infeld tails that are indeed strongly coupled, i.e., formally divergent for ordinary localized fluctuation fields and hence inequivalent to the canonical BornInfeld interactions. Focusing on classical solutions in special sectors (boundary conditions) one then discovers that their resummation is tantamount to regularizations of star products that require one to perform the field-theoretic calculations inside the twistor space and not just by looking at Taylor expansions. In other words, Vasiliev’s complete higher-spin...
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This document was uploaded on 09/28/2013.

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