Partially Massless Spin-2 Fields in String Generated Models

In cosmological backgrounds, there can be ’partially massless’ higher spin fields which have fewer degrees of freedom than their massive partners. The equations for the partially massless spin-2 fields are usually taken to be the linearized Einstein equations augmented with a ’tuned’ Pauli-Fierz mass. Here, we add more powers of curvatures and show that for the string-generated Einstein-Gauss-Bonnet model, partially massless spin-2 fields have real mass in AdS, in contrast to the Einstein level result. We discuss the implication of this for the AdS/CFT applications and briefly study the C-corrected AdS5 × S solution in type IIB SUGRA. e-mail: [email protected] In Anti-de-Sitter and de-Sitter spacetimes, massive higher spin fields ( s ≥ 2 ) exhibit a novel phenomenon: partial masslessness (or the appearance of extra gauge invariances), if the masses of the fields are ‘tuned’ to the background cosmological constant [1, 2, 3]. A massless spin-2 field (which we shall exclusively employ with here) in a flat D-dimensional background has D(D − 3)/2 degrees of freedom ( DOF) and a massive one has (D + 1)(D− 2)/2 DOF. On the other hand, in a constant curvature background there is a third possibility, for which the spin-2 field has one fewer than the generic massive case: Hence the name partially massless. A second derivative, scalar gauge invariance appears at the partially massless point. For these fields, there is a crucial difference between dS and the AdS spaces: The tuned m is positive for the former and negative for the latter. In the literature, the original analysis involves the equations of the linearized gravity augmented with the linear Pauli-Fierz mass term. In this note, we shall slightly generalize by considering also (the linearizations of ) higher curvature terms that are generated in certain string models and study their effects on the partially massless fields. The motivation for this work comes from the possible applications of partially massless spin-2 fields to AdS/CFT duality [4, 5, 6]. As is well-known, bulk fields in AdS correspond to operators in the boundary conformal field theory. According to the AdS/CFT dictionary, the masses of the bulk fields determine the conformal dimensions of the boundary fields. In particular, it was shown by Dolan et. al. [7], that partially massless spin-2 fields (hμν) in the bulk of AdS space correspond, on the boundary, to fields (Lij), which obey a specific conformally-invariant differential equation. If the boundary of the AdS is flat, the differential operator reduces to partial conservation equation of a tensor field (operator) : ∂i∂jL ij = 0. As demonstrated in [7], due to m being negative for partially massless fields in AdS, the first descendant of the corresponding partially conserved operator has a negative norm, rendering the boundary theory unphysical. Therefore, at the linear level there seems to be no room for the partially massless fields in AdS. For dS, on the other