Propagators forp-forms inAdS2p+1and correlation functions in theAdS7/(2,0)CFT correspondence

Abstract

In ${\mathrm{AdS}}_{2p+1}$ we construct propagators for p-forms whose Lagrangians contain terms of the form $A\ensuremath{\wedge}\mathrm{dA}.$ 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 ${\mathrm{AdS}}_{7}$ side of the ${\mathrm{AdS}}_{7}/(2,0)$ conformal field theory correspondence we compute the 2 and 3 point functions involving the self-dual tensor of the maximal 7D gauged supergravity (SUGRA), ${S}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}.$ Since the 7 dimensional antisymmetric self-dual tensor obeys first order field equations $(S+*dS=0),$ to get a nonvanishing 2 point function we add a 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 $\mathrm{SSB}$ and $SBB,$ describing vertex interactions with the gauge fields ${B}_{\ensuremath{\mu}}.$