A bound on massive higher spin particles

Abstract

According to common lore, massive elementary higher spin particles lead to inconsistencies when coupled to gravity. However, this scenario was not completely ruled out by previous arguments. In this paper, we show that in a theory where the low energy dynamics of the gravitons are governed by the Einstein-Hilbert action, any finite number of massive elementary particles with spin more than two cannot interact with gravitons, even classically, in a way that preserves causality. This is achieved in flat spacetime by studying eikonal scattering of higher spin particles in more than three spacetime dimensions. Our argument is insensitive to the physics above the effective cut-off scale and closes certain loopholes in previous arguments. Furthermore, it applies to higher spin particles even if they do not contribute to tree-level graviton scattering as a consequence of being charged under a global symmetry such as Z 2 . We derive analogous bounds in anti-de Sitter spacetime from analyticity properties of correlators of the dual CFT in the Regge limit. We also argue that an infinite tower of fine-tuned higher spin particles can still be consistent with causality. However, they necessarily affect the dynamics of gravitons at an energy scale comparable to the mass of the lightest higher spin particle. Finally, we apply the bound in de Sitter to impose restrictions on the structure of three-point functions in the squeezed limit of the scalar curvature perturbation produced during inflation.

Two-, three-, and four-body decays in the constructive standard model

“…In order to accomplish this reduction, we use standard momentum conservation, the on-shell conditions for both the spinors [see Eq. (15)] and squared momenta (p 2 i = m 2 i ) and the anticommutation properties for the momenta [see Eq. (38)].…”

A species or weak-gravity bound for large N gauge theories coupled to gravity

“…In particular, in the exact N = ∞ limit the mesons and glueballs behave as stable particles that are free and non-interacting [16][17][18]. This property of confining large N gauge theories will allow us to study the extension of the bound of [3] to higher spin mesons and glueballs.…”

“…More general constraints on massive higher spin particles can be derived from causality [3], ruling out some effective field theories and circumscribing the allowed UV completions of others. Consistent quantum field theories (QFTs) may also be constrained by rather different bounds relating to the total number of particle species [4][5][6][7][8][9] or the relative strength of the gravitational force [10].…”

“…Much of our discussion will concern the distinction between fundamental and composite particles, as our goal is to establish when the bounds of [3] apply to composites.…”

“…The outline of this paper is as follows. In section 2 we provide abbreviated reviews of large N scalings and the causality bounds of [3,[11][12][13]15]. In section 3 we critically examine the AdS/CFT causality constraints to understand if and when they should apply to composite particles.…”