universe Article The ABC of Higher-Spin AdS/CFT Simone Giombi 1,* Igor R. Klebanov 1,2 and Zhong Ming Tan 1,3 1 Department of Physics, Princeton University, Princeton, NJ 08544, USA;
[email protected] (I.R.K.);
[email protected] (Z.M.T.) 2 Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA 3 Département de Physique, École Normale Supérieure, 45 rue d’Ulm, 75005 Paris, France * Correspondence:
[email protected] Received: 27 October 2017; Accepted: 11 December 2017; Published: 19 January 2018 Abstract: In recent literature, one-loop tests of the higher-spin AdSd+1/CFTd correspondences were carried out. Here, we extend these results to a more general set of theories in d > 2. First, we consider the Type B higher spin theories, which have been conjectured to be dual to CFTs consisting of the singlet sector of N free fermion fields. In addition to the case of N Dirac fermions, we carefully study the projections to Weyl, Majorana, symplectic and Majorana–Weyl fermions in the dimensions where they exist. Second, we explore theories involving elements of both Type A and Type B theories, which we call Type AB. Their spectrum includes fields of every half-integer spin, and they are expected to be related to the U(N)/O(N) singlet sector of the CFT of N free complex/real scalar and fermionic fields. Finally, we explore the Type C theories, which have been conjectured to be dual to d the CFTs of p-form gauge fields, where p = 2 − 1. In most cases, we find that the free energies at O(N0) either vanish or give contributions proportional to the free-energy of a single free field in the conjectured dual CFT.