Propagators for massive symmetric tensor and p-forms in AdS(d+1)

TL;DR

This work constructs explicit bulk-to-bulk propagators for massive $p$-forms and massive symmetric tensors in Euclidean $AdS_{d+1}$. By employing a bi-tensor ansatz that separates physical and pure-gauge parts, the authors reduce the problem to scalar propagators with effective masses $oldsymbol{m μ}^2 = m^2 - p(d-p)$ for $p$-forms and $oldsymbol{m μ}^2 = m_1^2$ for the massive symmetric tensor, solving via hypergeometric functions with $oldsymbol{m Δ} = rac{d}{2} + rac{1}{2}igl(d^2 + 4oldsymbol{m μ}^2igr)^{1/2}$. They provide complete expressions for the propagators in terms of invariant bi-tensors, along with derivative-integral relations that fix all auxiliary functions, and verify that the short-distance behavior matches the flat-space limits. The results supply the necessary Green functions for computing bulk-to-bulk correlators in AdS/CFT for massive fields and ensure consistency with flat-space physics in the appropriate limit. Overall, the paper extends prior massless/gauge-fixed propagator constructions to the massive regime with explicit, hypergeometric-structured solutions and consistent short-distance limits.

Abstract

We construct propagators in Euclidean AdS(d+1) space-time for massive p-forms and massive symmetric tensors.