Nonlocal born infeld tail that is a strongly coupled

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Unformatted text preview: of Weyl tensors and their derivatives that cannot be replaced by a single effective Born-Infeld interaction with a finite coupling; and (iii) constrain the spectrum and cubic couplings by solving higher-order consistency conditions in the g expansion (starting at quartic order). However, without any guiding principle other than Lorentz and gauge invariance, this is an a priori intractable problem essentially due to the fact that the whole cubic tail must be fixed, which may require going to very high orders in the Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . g expansion. Of course, in the simplest scenario, the complete cubic action could be fixed by quartic consistency, in which case there would be no interaction ambiguity at the cubic level. Thus, of all possible hypothetical outcomes the extreme cases are (i) quartic consistency suffices to completely fix the cubic action including its Born-Infeld tail; and (ii) quartic consistency rules out the cubic action altogether in which case the choice of free theory initiating the Fronsdal program would have to be revised. In summary, to make the situation more tractable, one may resort to some additional guidance besides Lorentz and gauge invariance, or bias if one wishes to use that word, on what are suitable notions for ‘‘higher-spin multiplets,’’ for selection of spectrum of fields, and ‘‘higher-spin tensor calculus,’’ for construction of interactions. How to proceed with this issue becomes most clear in higher-spin gravity: higher-spin gauge theories based on higher-spin algebras given by infinite-dimensional extensions of ordinary finite-dimensional spacetime isometry algebras. At this stage it is natural to rethink how unitary representations of the complete higher-spin algebra are mapped directly to fields living in infinite-dimensional geometries containing ordinary spacetime as a submanifold. Indeed one of the key instruments going into Vasiliev’s formulation of fully nonlinear equations of motion for higher-spin gravities is unfolded dynamics (Vasiliev, 1988, 1989, 1990, 1994): a mathematically precise tool for manifestly diffeomorphisminvariant generalized spacetime reconstructions applying to finite-dimensional as well as infinite-dimensional cases. C. Vasiliev’s equations A working definition of higher-spin algebras developed by Fradkin, Konstein, and Vasiliev (Fradkin and Vasiliev, 1987a, 1988; Konshtein and Vasiliev, 1989, 1990) that has proven to be useful is that of Lie subalgebras of associative algebras obtained from the enveloping algebras of the spacetime isometry algebra by factoring out annihilators of their ‘‘fundamental,’’ or ultrashort, unitary representations (singletons). In this setting, the higher-spin generators are monomials in the spacetime isometry generators, and higher-spin multiplets arise by tensoring together singletons (Flato and Fronsdal, 1978; Vasiliev, 2004c;...
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This document was uploaded on 09/28/2013.

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