One-loop tests of the supersymmetric higher spin AdS4/CFT3 correspondence

Yi Pang, Ergin Sezgin, and Yaodong Zhu
Phys. Rev. D 95, 026008 – Published 11 January 2017

Abstract

We compute one-loop free energy for D=4 Vasiliev higher spin gravities based on Konstein-Vasiliev algebras hu(m;n|4), ho(m;n|4), or husp(m;n|4) and subject to higher spin-preserving boundary conditions, which are conjectured to be dual to the U(N), O(N) or USp(N) singlet sectors, respectively, of free conformal field theories (CFTs) on the boundary of AdS4. Ordinary supersymmetric higher spin theories appear as special cases of Konstein-Vasiliev theories, when the corresponding higher spin algebra contains OSp(N|4) as a subalgebra. In AdS4 with an S3 boundary, we use a regularization scheme for individual spins that employs their character such that the subsequent sum over all spins is finite, thereby avoiding the need for additional regularization. We find that the contribution of the infinite tower of bulk fermions vanishes. As a result, the free energy is the sum of those which arise in type A and type B models with internal symmetries, the known mismatch between the bulk and boundary free energies for type B model persists, and ordinary supersymmetric higher spin theories exhibit the mismatch as well. The only models that have a match are type A models with internal symmetries, corresponding to n=0. The matching requires identification of the inverse Newton constant GN1 with N plus a proper integer as was found previously for special cases. In AdS4 with an S1×S2 boundary, the bulk one-loop free energies match those of the dual free CFTs for arbitrary m and n. We also show that a supersymmetric double-trace deformation of free CFT based on OSp(1|4) does not contribute to the O(N0) free energy, as expected from the bulk.

  • Received 15 November 2016

DOI:https://doi.org/10.1103/PhysRevD.95.026008

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsGravitation, Cosmology & Astrophysics

Authors & Affiliations

Yi Pang1,*, Ergin Sezgin2,†, and Yaodong Zhu2,‡

  • 1Max-Planck-Insitut für Gravitationsphysik (Albert-Einstein-Institut) Am Mühlenberg 1, DE-14476 Potsdam, Germany
  • 2George and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA

  • *yi.pang@aei.mpg.de
  • sezgin@physics.tamu.edu
  • yaodongmatt@physics.tamu.edu

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Issue

Vol. 95, Iss. 2 — 15 January 2017

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