Limiting shifted homotopy in higher-spin theory and spin-locality
A bstract 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 ind...
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Published in | The journal of high energy physics Vol. 2019; no. 12; pp. 1 - 51 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.12.2019
Springer Nature B.V SpringerOpen |
Subjects | |
Online Access | Get full text |
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Summary: | A
bstract
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 𝜂
2
and
η
¯
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
¯
.
Also the 𝜂
2
and
η
¯
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
¯
.
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. |
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ISSN: | 1029-8479 1029-8479 |
DOI: | 10.1007/JHEP12(2019)086 |