Inconsistency of point-particle dynamics on higher-spin backgrounds

Abstract: We use the light-cone gauge formalism to study interactions of point particles with massless higher-spin fields. By analysing the light-cone consistency conditions at the subleading order in higher-spin fields, we find that no local interactions of point particles with chiral higher-spin fields are possible. Considering that chiral higher-spin theories form inevitable closed subsectors of any consistent massless higher-spin theories in flat space, this conclusion holds more generally, in particular, it applies to putative parity-invariant completions of chiral higher-spin theories. Besides that, we argue that our result implies that Riemannian geometry cannot be extended to spaces with non-trivial higher-spin fields, in particular, there is no higher-spin extension of space-time interval. In the present paper we focus on a case of a massless particle, while a more technical massive case will be analysed in a companion paper.

Inconsistency of Point Particle's Dynamics on Higher-Spin Backgrounds

In this paper, Ivanovskiy and Ponomarev address a critical issue in the study of higher-spin (HS) dynamics: the interaction of point particles with HS fields under the light-cone gauge formalism. Higher-spin theories are extensions of gravity that incorporate massless fields of spin greater than two, potentially improving quantum gravity's properties by leveraging their extensive symmetries. However, constructing consistent HS interactions in flat space is fraught with difficulties, as highlighted by several no-go theorems. This paper focuses on chiral HS theories, which are prominent due to their manifest locality and similarity to theories such as self-dual Yang-Mills.

The core of the paper is dedicated to analyzing consistency conditions on the interactions between point particles and HS fields at the subleading order. It is established that no local interactions compatible with light-cone consistency conditions are possible between point particles and chiral HS fields. This negative result is significant because chiral HS theories are subsets of any consistent HS theory in flat space, suggesting broader implications.

Three key constraints are derived from the commutation relations of Poincare generators: $[P^-,J^{x-}] = 0$, $[P^-,J^{\bar x-}]=0$, and $[J^{x-},J^{\bar x-}]=0$. By examining these constraints perturbatively, the authors demonstrate that HS fields cannot couple consistently with scalar point particles in four-dimensional Minkowski space. The analysis relies heavily on the algebraic properties of the terms within these constraints relative to the light-cone phase space formalism.

The implications of this finding are profound. Notably, it suggests that the extension of Riemannian geometry to encompass spaces with non-trivial HS fields is untenable. Consequently, observations and constructs analogous to spacetime intervals in HS scenarios remain undefined. The paper also points out that this inconsistency rules out direct application of Finsler geometry or Segal's symplectic approaches in HS contexts.

The insights from this paper prompt further research into HS geometries and interactions, particularly exploring spinning particle systems that might circumvent the limitations identified for scalar point particles. The authors propose the intriguing possibility of consistent spinning particle interactions with HS fields, given symplectic realizations of HS algebras. Such investigations could advance the theoretical framework required for valid HS geometry interpretations and may influence future AI developments in understanding complex field theory models.

For researchers focused on HS theories, this paper offers a meticulous examination of particle-field interactions, systematically dismantling intuitive assumptions about straightforward couplings. The rigorous use of the light-cone formalism, combined with addressing the interrelation of algebraic symmetries, embodies a robust approach for further explorations into HS dynamical systems and quantum gravity models.