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

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.