On four-point interactions in massless higher spin theory in flat space

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Title: On four-point interactions in massless higher spin theory in flat space
Authors: Roiban, R
Tseytlin, AA
Item Type: Journal Article
Abstract: We consider a minimal interacting theory of a single tower of spin j = 0, 2, 4,… massless Fronsdal fields in flat space with local Lorentz-covariant cubic interaction vertices. We address the question of constraints on possible quartic interaction vertices imposed by the condition of on-shell gauge invariance of the tree-level four-point scattering amplitudes involving three spin 0 and one spin j particle. We find that these constraints admit a local solution for quartic 000j interaction term in the action only for j = 2 and j = 4. We determine the non-local terms in four-vertices required in the j ≥ 6 case and suggest that these non-localities may be interpreted as a result of integrating out a tower of auxiliary ghost-like massless higher spin fields in an extended theory with a local action, up to possible higher-point interactions of the ghost fields. We also consider the conformal off-shell extension of the Einstein theory and show that the perturbative expansion of its action is the same as that of the non-local action resulting from integrating out the trace of the graviton field from the Einstein action. Motivated by this example, we conjecture the existence of a similar conformal off-shell extension of a massless higher spin theory that may be related to the above extended theory. It may then have the same infinite-dimensional symmetry as the higher-derivative conformal higher spin theory and may thus lead to a trivial S matrix.
Issue Date: 26-Apr-2017
Date of Acceptance: 22-Apr-2017
ISSN: 1029-8479
Publisher: SPRINGER
Volume: 2017
Issue: 4
Copyright Statement: © 2017 The Author(s). Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0, which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Sponsor/Funder: Commission of the European Communities
Science and Technology Facilities Council (STFC)
Funder's Grant Number: 290456
Keywords: Science & Technology
Physical Sciences
Physics, Particles & Fields
Conformal and W Symmetry
Higher Spin Symmetry
Anomalies in Field and String Theories
Higher Spin Gravity
01 Mathematical Sciences
02 Physical Sciences
Publication Status: Published
Open Access location:
Article Number: ARTN 139
Appears in Collections:Physics
Theoretical Physics

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