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One Loop Tests of Supersymmetric Higher Spin AdS4/CFT3

Pang, Y., Sezgin, E., & Zhu, Y. (2017). One Loop Tests of Supersymmetric Higher Spin AdS4/CFT3. Physical Review D, 95: 026008. doi:10.1103/PhysRevD.95.026008.

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Genre: Journal Article

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1608.07298.pdf (Preprint), 446KB
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Creators:
Pang, Yi1, Author
Sezgin, Ergin, Author
Zhu, Yaodong, Author
Affiliations:
1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008

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Free keywords: High Energy Physics - Theory, hep-th
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 CFTs on the boundary of $AdS_4$. Ordinary supersymmetric higher spin theories appear as special cases of Konstein-Vasiliev theories, when the corresponding higher spin algebra contains $OSp({\cal N}|4)$ as subalgebra. In $AdS_4$ with $S^3$ boundary, we use a modified spectral zeta function method, which avoids the ambiguity arising from summing over infinite number of spins. 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's constant $G_N^{-1}$ with $N$ plus a proper integer as was found previously for special cases. In $AdS_4$ with $S^1\times S^2$ 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 ${\cal O}(N^0)$ free energy, as expected from the bulk.

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Dates: 2016-08-252017
Publication Status: Published in print
Pages: 30 pages
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1608.07298
URI: http://arxiv.org/abs/1608.07298
DOI: 10.1103/PhysRevD.95.026008
Degree: -

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Title: Physical Review D
Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 95 Sequence Number: 026008 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258