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 log-divergent 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.
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Brust, C., Hinterbichler, K. Partially massless higher-spin theory II: one-loop effective actions. J. High Energ. Phys. 2017, 126 (2017). https://doi.org/10.1007/JHEP01(2017)126
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DOI: https://doi.org/10.1007/JHEP01(2017)126