TY - JOUR
T1 - The ABC of higher-spin AdS/CFT
AU - Giombi, Simone
AU - Klebanov, Igor R.
AU - Tan, Zhong Ming
N1 - Funding Information:
Acknowledgments: The work of SG was supported in part by the U.S. NSF under Grants No. PHY-1318681 and PHY-1620542. The work of IRK was supported in part by the U.S. NSF under Grants No. PHY-1314198 and PHY-1620059. The work of ZMT was supported in part by the École Normale Supérieure, France under the grant LabEx ENS-ICFP: ANR-10-LABX-0010/ANR-10-IDEX-0001-02 PSL, and the Public Service Commission, Singapore. Parts of this paper are based on ZMT’s Princeton University 2014 undergraduate thesis. IRK thanks the Niels Bohr International Academy for hospitality during the final stages of his work on this paper.
Publisher Copyright:
© 2018 by the authors.
PY - 2018/1
Y1 - 2018/1
N2 - In recent literature, one-loop tests of the higher-spin AdS d + 1 /CFT d 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 the CFTs of p-form gauge fields, where p = d 2 − 1. In most cases, we find that the free energies at O(N 0 ) either vanish or give contributions proportional to the free-energy of a single free field in the conjectured dual CFT. Interpreting these non-vanishing values as shifts of the bulk coupling constant G N ∼ 1/(N − k), we find the values k = −1, −1/2, 0, 1/2, 1, 2. Exceptions to this rule are the Type B and AB theories in odd d; for them, we find a mismatch between the bulk and boundary free energies that has a simple structure, but does not follow from a simple shift of the bulk coupling constant.
AB - In recent literature, one-loop tests of the higher-spin AdS d + 1 /CFT d 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 the CFTs of p-form gauge fields, where p = d 2 − 1. In most cases, we find that the free energies at O(N 0 ) either vanish or give contributions proportional to the free-energy of a single free field in the conjectured dual CFT. Interpreting these non-vanishing values as shifts of the bulk coupling constant G N ∼ 1/(N − k), we find the values k = −1, −1/2, 0, 1/2, 1, 2. Exceptions to this rule are the Type B and AB theories in odd d; for them, we find a mismatch between the bulk and boundary free energies that has a simple structure, but does not follow from a simple shift of the bulk coupling constant.
KW - 1/N expansion
KW - AdS/CFT correspondence
KW - Higher-Spin Symmetry
UR - http://www.scopus.com/inward/record.url?scp=85047527883&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85047527883&partnerID=8YFLogxK
U2 - 10.3390/universe4010018
DO - 10.3390/universe4010018
M3 - Article
AN - SCOPUS:85047527883
SN - 2218-1997
VL - 4
JO - Universe
JF - Universe
IS - 1
M1 - 18
ER -