Partially massless higher-spin theory II: one-loop effective actions

Abstract

We continue our study of a generalization of the D-dimensional linearized Vasiliev higher-spin equations to include a tower of partially massless (PM) fields. We compute one-loop effective actions by evaluating zeta functions for both the "minimal" and "non-minimal" parity-even versions of the theory. Specifically, we compute the logdivergent part of the effective action in odd-dimensional Euclidean AdS spaces for D = 7 through 19 (dual to the a-type conformal anomaly of the dual boundary theory), and the finite part of the effective action in even-dimensional Euclidean AdS spaces for D = 4 through 8 (dual to the free energy on a sphere of the dual boundary theory). We pay special attention to the case D = 4, where module mixings occur in the dual field theory and subtlety arises in the one-loop computation. The results provide evidence that the theory is UV complete and one-loop exact, and we conjecture and provide evidence for a map between the inverse Newton's constant of the partially massless higher-spin theory and the number of colors in the dual CFT.

Character integral representation of zeta function in AdSd+1. Part I. Derivation of the general formula

“…More precisely, we seek for the formula extending the CIRZ in AdS d+1 with arbitrary integer d ≥ 2. Although the dimensional dependence in higher-spin gravity is rather minimal, most of the results in the literature [9,10,[24][25][26][27] concern only specific dimensions for technical reasons, except in [23] where the results of the type-A higher-spin gravity are extended to arbitrary (non-integer) dimensions. From the viewpoint of physical applications, one might not need to care about higher dimensions yet, but it is at the same time tempting to obtain results with parametric dependence on d. As usual, generalities may provide new and valuable lessons on what is considered to be well-understood.…”

Character integral representation of zeta function in AdSd+1. Part II. Application to partially-massless higher-spin gravities

“…The choice we make is the replacement after full decomposition of the logarithms. See e.g [46]. and references therein.…”

Theory for multiple partially massless spin-2 fields

“…It is indeed an outstanding field theoretical problem to determine what theories containing PM fields may in principle be written purely on the basis of consistency, and our construction is a step forward in this program. Regarding the applicability of our model of multiple PM spin-2 particles, it would be interesting to see whether it could be embedded into a higher-spin theory that should in turn provide an extension of the higher-spin model proposed in [7] and discussed later in [8,9]. This theory is of interest as it has been conjectured to be dual to the O(N ) model at a multicritical isotropic Lifshitz point (see [39] for a review).…”