Propagators for p-forms in AdS_{2p+1} and correlation functions in the AdS_7/(2,0) CFT correspondence

TL;DR

This paper constructs propagators for p-forms in AdS_{2p+1}, explores their properties, and computes correlation functions involving self-dual tensors in the AdS_7/(2,0) CFT correspondence, revealing new tensor structures.

Contribution

It introduces a complete set of propagators for p-forms in odd-dimensional AdS spaces, including a previously overlooked bitensor, and computes specific correlation functions in the AdS_7/(2,0) setup.

Findings

New propagators for p-forms in AdS_{2p+1} with topological terms

Identification of an additional bitensor affecting propagator formulas

Explicit 2- and 3-point functions involving self-dual tensors in AdS_7/CFT_6

Abstract

In AdS_{2p+1} we construct propagators for p-forms whose lagrangians contain terms of the form A / d A. In particular we explore the case of forms satisfying ``self duality in odd dimensions'', and the case of forms with a topological mass term. We point out that the ``complete'' set of maximally symmetric bitensors previously used in all the other propagator papers is incomplete - there exists another bitensor which can and does appear in the formulas for the propagators in this particular case. Nevertheless, its presence does not affect the other propagators computed so far. On the AdS side of the correspondence we compute the 2 and 3 point functions involving the self-dual tensor of the maximal 7d gauged supergravity (sugra), S_{\mu\nu\rho}. Since the 7 dimensional antisymmetric self-dual tensor obeys first order field equations (S + * d S=0), to get a nonvanishing 2 point function we add a certain boundary term (to satisfy the variational principle on a manifold with boundary) to the 7d action. The 3 point functions we compute are of the type SSB and SBB, describing vertex interactions with the gauge fields B_{\mu}.