One loop tests of higher spin AdS/CFT

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Vasiliev's type A higher spin theories in AdS4 have been conjectured to be dual to the U(N) or O (N0) singlet sectors in 3-d conformal field theories with N -component scalar fields. We compare the O (N0) correction to the 3-sphere free energy F in the CFTs with corresponding calculations in the higher spin theories. This requires evaluating a regularized sum over one loop vacuum energies of an infinite set of massless higher spin gauge fields in Euclidean AdS4. For the Vasiliev theory including fields of all integer spin and a scalar with Δ = 1 boundary condition, we show that the regularized sum vanishes. This is in perfect agreement with the vanishing of subleading corrections to F in the U(N) singlet sector of the theory of N free complex scalar fields. For the minimal Vasiliev theory including fields of only even spin, the regularized sum remarkably equals the value of F for one free real scalar field. This result may agree with the O(N) singlet sector of the theory of N real scalar fields, provided the coupling constant in the Vasiliev theory is identified as GN ∼ 1/(N - 1). Similarly, consideration of the USp(N) singlet sector for N complex scalar fields, which we conjecture to be dual to the husp(2; 0|4) Vasiliev theory, requires GN ∼ 1/(N + 1). We also test the higher spin AdS 3/CFT2 conjectures by calculating the regularized sum over one loop vacuum energies of higher spin fields in AdS3. We match the result with the O (N0) term in the central charge of the W N minimal models; this requires a certain truncation of the CFT operator spectrum so that the bulk theory contains two real scalar fields with the same boundary conditions.

Original languageEnglish (US)
Article number68
JournalJournal of High Energy Physics
Issue number12
StatePublished - Dec 2013

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • 1/N expansion
  • AdS-CFT correspondence
  • Models of quantum gravity


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