The propagator for a general form field in $AdS_{d+1}$

TL;DR

This paper derives the propagator equations for p-form fields in AdS_{d+1} using Poincare duality, providing a unified framework for both massless and massive forms across various dimensions.

Contribution

It introduces a general method to obtain p-form propagators in AdS spaces based on duality relations and linear equations in dimension, extending previous specific cases.

Findings

Derived propagator equations for p-forms in AdS_{d+1}

Conjectured and verified Poincare duality formulas for forms

Unified approach applicable to massless and massive p-forms

Abstract

Using the known propagator equations for 0,1 and 2 forms in AdS_{d+1}, we find the p-form field propagator equations in dimensions where the forms are Poincare dual. Since the general equation obeyed by the propagators is linear in dimension, this gives us the equation obeyed by the propagators for any d. Furthermore, based on the Poincare duality formulas for 0,1,2 and 3 forms we conjecture the general form of the Poincare duality formulas, and check them against the previously found propagator equations. The whole structure is self-consistent. Once we have the equations, we can easily obtain all the p-form field propagators in AdS_{d+1}. The generalization to massive p-forms can also be easily done.