53 research outputs found
Canonical Effective Subalgebras of Classical Algebras as Constructive Metric Completions
We prove general theorems about unique existence of effective subalgebras of classical algebras. The theorems are consequences of standard facts about completions of metric spaces within the framework of constructive mathematics, suitably interpreted in realizability models. We work with general realizability models rather than with a particular model of computation. Consequently, all the results are applicable in various established schools of computability, such as type 1 and type 2 effectivity, domain representations, equilogical spaces, and others
How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
Aiming at non-experts, we explain the key mechanisms of higher-spin
extensions of ordinary gravity. We first overview various no-go theorems for
low-energy scattering of massless particles in flat spacetime. In doing so we
dress a dictionary between the S-matrix and the Lagrangian approaches,
exhibiting their relative advantages and weaknesses, after which we high-light
potential loop-holes for non-trivial massless dynamics. We then review positive
yes-go results for non-abelian cubic higher-derivative vertices in constantly
curved backgrounds. Finally we outline how higher-spin symmetry can be
reconciled with the equivalence principle in the presence of a cosmological
constant leading to the Fradkin--Vasiliev vertices and Vasiliev's higher-spin
gravity with its double perturbative expansion (in terms of numbers of fields
and derivatives).Comment: LaTeX, 50 pages, minor changes, many refs added; version accepted for
publication in Reviews of Modern Physic
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