Journal of High Energy Physics

, 2017:126 | Cite as

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

  • Christopher Brust
  • Kurt HinterbichlerEmail author
Open Access
Regular Article - Theoretical Physics


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.


Higher Spin Gravity Higher Spin Symmetry AdS-CFT Correspondence 


Open Access

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.CERCA, Department of PhysicsCase Western Reserve UniversityClevelandU.S.A.

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