Formal higher-spin theories and Kontsevich–Shoikhet–Tsygan formality
| Autor: | Alexey A. Sharapov, Evgeny Skvortsov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
High Energy Physics - Theory
Physics Nuclear and High Energy Physics Pure mathematics 010308 nuclear & particles physics Algebraic structure Structure (category theory) FOS: Physical sciences Formality 01 natural sciences Cohomology Interpretation (model theory) AdS/CFT correspondence High Energy Physics - Theory (hep-th) Mathematics::K-Theory and Homology Mathematics::Quantum Algebra 0103 physical sciences lcsh:QC770-798 lcsh:Nuclear and particle physics. Atomic energy. Radioactivity Invariant (mathematics) 010306 general physics Symplectic geometry |
| Zdroj: | Nuclear Physics B, Vol 921, Iss C, Pp 538-584 (2017) Nuclear Physics B |
| ISSN: | 1873-1562 0550-3213 |
| Popis: | The formal algebraic structures that govern higher-spin theories within the unfolded approach turn out to be related to an extension of the Kontsevich Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one to construct the Hochschild cocycles of higher-spin algebras that make the interaction vertices. As an application of these results we construct a family of Vasiliev-like equations that generate the Hochschild cocycles with $sp(2n)$ symmetry from the corresponding cycles. A particular case of $sp(4)$ may be relevant for the on-shell action of the $4d$ theory. We also give the exact equations that describe propagation of higher-spin fields on a background of their own. The consistency of formal higher-spin theories turns out to have a purely geometric interpretation: there exists a certain symplectic invariant associated to cutting a polytope into simplices, namely, the Alexander-Spanier cocycle. Comment: typos fixed, many comments added, 36 pages + 20 pages of Appendices, 3 figures |
| Databáze: | OpenAIRE |
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