AdS S-Matrix for Massive Vector Fields

TL;DR

This paper extends the AdS S-matrix framework to massive vector fields, deriving propagators and computing scattering amplitudes in AdS, with applications to the Abelian Higgs Model and potential massless limits.

Contribution

It introduces a generalized AdS S-matrix formulation for massive vectors, including derivation of propagators and explicit scattering amplitude calculations.

Findings

Derived massive vector bulk-to-boundary and bulk-to-bulk propagators.

Computed the AdS S-matrix for vector scattering mediated by scalars.

Discussed the massless limit of propagators within the perturbative framework.

Abstract

We generalize a recent ``AdS S-matrix" formulation for interacting massive scalars on AdS spacetimes to the case of massive vector fields. This method relies on taking the infinite radius limit for scattering processes perturbatively, which is analyzed using Witten diagrams in the momentum space formulation of global AdS with embedding space coordinates. It recovers the S-matrix with subleading corrections in powers of the inverse AdS radius about a flat spacetime region within the bulk. We first derive the massive vector bulk-to-boundary and bulk-to-bulk propagators within this perturbation theory. As an example, we consider the Abelian Higgs Model in a certain regime of the coupling parameter space to model an interacting Proca theory on AdS spacetimes. We specifically compute the AdS S-matrix for a process involving massive external vector fields mediated by a massive scalar. We lastly discuss possible massless limit of propagators within this perturbative framework.