Limiting shifted homotopy in higher-spin theory and spin-locality
Abstract Higher-spin vertices containing up to quintic interactions at the LagTangian level are explicitly calculated in the one-form sector of the non-linear unfolded higher-spin equations using a 𝛽 →-∞-shifted contracting homotopy introduced in the paper. The problem is solved in a background inde...
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Online Access: | https://doi.org/10.1007/JHEP12(2019)086 |
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doaj-fb5db973f1a84a7b9529a163e1f238392020-12-13T12:05:53ZengSpringerOpenJournal of High Energy Physics1029-84792019-12-0120191215110.1007/JHEP12(2019)086Limiting shifted homotopy in higher-spin theory and spin-localityV.E. Didenko0O.A. Gelfond1A.V. Korybut2M.A. Vasiliev3TK Tamm Department of Theoretical Physics, Lebedev Physical InstituteTK Tamm Department of Theoretical Physics, Lebedev Physical InstituteTK Tamm Department of Theoretical Physics, Lebedev Physical InstituteTK Tamm Department of Theoretical Physics, Lebedev Physical InstituteAbstract Higher-spin vertices containing up to quintic interactions at the LagTangian level are explicitly calculated in the one-form sector of the non-linear unfolded higher-spin equations using a 𝛽 →-∞-shifted contracting homotopy introduced in the paper. The problem is solved in a background independent way and for any value of the complex parameter 𝜂 in the higher-spin equations. All obtained vertices are shown to be spin-local containing a finite number of derivatives in the spinor space for any given set of spins. The vertices proportional to 𝜂2 and η ¯ 2 $$ {\overline{\eta}}^2 $$ are in addition ultra-local, i.e., zero-forms that enter into the vertex in question are free from the dependence on at least one of the spinor variables y or y ¯ $$ \overline{y} $$ . Also the 𝜂2 and η ¯ 2 $$ {\overline{\eta}}^2 $$ vertices are shown to vanish on any purely gravitational background hence not contributing to the higher-spin current interactions on AdS 4 . This implies in particular that the gravitational constant in front of the stress tensor is positive being proportional to η η ¯ $$ \eta \overline{\eta} $$ . It is shown that the 𝛽-shifted homotopy technique developed in this paper can be reinterpreted as the conventional one but in the 𝛽-dependent deformed star product.https://doi.org/10.1007/JHEP12(2019)086Higher Spin GravityHigher Spin SymmetryGauge-gravity correspondence |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
V.E. Didenko O.A. Gelfond A.V. Korybut M.A. Vasiliev |
spellingShingle |
V.E. Didenko O.A. Gelfond A.V. Korybut M.A. Vasiliev Limiting shifted homotopy in higher-spin theory and spin-locality Journal of High Energy Physics Higher Spin Gravity Higher Spin Symmetry Gauge-gravity correspondence |
author_facet |
V.E. Didenko O.A. Gelfond A.V. Korybut M.A. Vasiliev |
author_sort |
V.E. Didenko |
title |
Limiting shifted homotopy in higher-spin theory and spin-locality |
title_short |
Limiting shifted homotopy in higher-spin theory and spin-locality |
title_full |
Limiting shifted homotopy in higher-spin theory and spin-locality |
title_fullStr |
Limiting shifted homotopy in higher-spin theory and spin-locality |
title_full_unstemmed |
Limiting shifted homotopy in higher-spin theory and spin-locality |
title_sort |
limiting shifted homotopy in higher-spin theory and spin-locality |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2019-12-01 |
description |
Abstract Higher-spin vertices containing up to quintic interactions at the LagTangian level are explicitly calculated in the one-form sector of the non-linear unfolded higher-spin equations using a 𝛽 →-∞-shifted contracting homotopy introduced in the paper. The problem is solved in a background independent way and for any value of the complex parameter 𝜂 in the higher-spin equations. All obtained vertices are shown to be spin-local containing a finite number of derivatives in the spinor space for any given set of spins. The vertices proportional to 𝜂2 and η ¯ 2 $$ {\overline{\eta}}^2 $$ are in addition ultra-local, i.e., zero-forms that enter into the vertex in question are free from the dependence on at least one of the spinor variables y or y ¯ $$ \overline{y} $$ . Also the 𝜂2 and η ¯ 2 $$ {\overline{\eta}}^2 $$ vertices are shown to vanish on any purely gravitational background hence not contributing to the higher-spin current interactions on AdS 4 . This implies in particular that the gravitational constant in front of the stress tensor is positive being proportional to η η ¯ $$ \eta \overline{\eta} $$ . It is shown that the 𝛽-shifted homotopy technique developed in this paper can be reinterpreted as the conventional one but in the 𝛽-dependent deformed star product. |
topic |
Higher Spin Gravity Higher Spin Symmetry Gauge-gravity correspondence |
url |
https://doi.org/10.1007/JHEP12(2019)086 |
work_keys_str_mv |
AT vedidenko limitingshiftedhomotopyinhigherspintheoryandspinlocality AT oagelfond limitingshiftedhomotopyinhigherspintheoryandspinlocality AT avkorybut limitingshiftedhomotopyinhigherspintheoryandspinlocality AT mavasiliev limitingshiftedhomotopyinhigherspintheoryandspinlocality |
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1724385368017469440 |