On triviality of S-matrix in conformal higher spin theory

Abstract

We consider the conformal higher spin (CHS) theory in d=4 that contains the s=1 Maxwell vector, s=2 Weyl graviton and their higher spin s=3,4,... counterparts with higher-derivative \box^s kinetic terms. The interacting action for such theory can be found as the coefficient of the logarithmically divergent part in the induced action for sources coupled to higher spin currents in a free complex scalar field model. We explicitly determine some cubic and quartic interaction vertices in the CHS action from scalar loop integrals. We then compute the simplest tree-level 4-particle scattering amplitudes 11 -> 11, 22 -> 22 and 11 -> 22 and find that after summing up all the intermediate CHS exchanges they vanish. This generalises the vanishing of the scattering amplitude for external conformal scalars interacting via the exchange of all CHS fields found earlier in arXiv:1512.08896. This vanishing should generalise to all scattering amplitudes in the CHS theory and as in the conformal scalar scattering case should be a consequence of the underlying infinite dimensional higher spin symmetry that extends the standard conformal symmetry.

32 pages. v2, v3: minor corrections and references added

References in corpus (5)

• Einstein Gravity from Conformal Gravity
• Effective action in a higher-spin background
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Partition function of free conformal higher spin theory
• Conformal Supergravity Tree Amplitudes from Open Twistor String Theory

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• Toward a twistor action for chiral higher-spin gravity
• Higher-spin Yang-Mills, amplitudes and self-duality
• Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes
• $C_T$ for conformal higher spin fields from partition function on conically deformed sphere
• Higher Spin Gravities and Presymplectic AKSZ Models
• Constraining higher-spin S-matrices
• Higher-spin Cotton tensors and massive gauge-invariant actions in AdS${}_3$
• Induced action for superconformal higher-spin multiplets using SCFT techniques
• Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes