Scalar scattering via conformal higher spin exchange
E. Joung, S. Nakach, A. A. Tseytlin
TL;DR
This work studies a flat-space model where massless scalars couple to an infinite tower of conformal higher spin (CHS) fields. It derives the tree-level four-scalar amplitude by summing CHS-spin exchanges and finds the amplitude vanishes for generic kinematics when the sum over spins is regularized in a symmetry-preserving way. The authors connect this vanishing to the global CHS symmetry, providing a symmetry-based justification for the spin-sum prescription. At one loop, they analyze the UV-divergent part of the four-scalar amplitude in a constant h_0 background, separating physical and ghost contributions and showing a regulator-dependent, nontrivial sum over spins; the overall cancellation is not guaranteed, highlighting subtle issues in CHS quantum consistency and the need for further study of anomalies. Overall, the paper argues for a highly constrained, symmetry-protected structure in CHS theories, with potential implications for the consistency of infinite-spin extensions and their S-matrices.”
Abstract
Theories containing infinite number of higher spin fields require a particular definition of summation over spins consistent with their underlying symmetries. We consider a model of massless scalars interacting (via bilinear conserved currents) with conformal higher spin fields in flat space. We compute the tree-level four-scalar scattering amplitude using a natural prescription for summation over an infinite set of conformal higher spin exchanges and find that it vanishes (modulo delta-function terms having support on measure-zero domain in phase space). Independently, we show that this vanishing of the scalar scattering amplitude is, in fact, implied by the global conformal higher spin symmetry of this model. We also discuss one-loop corrections to the four-scalar scattering amplitude.