The ABC of Higher-Spin AdS/CFT

Giombi, Simone; Klebanov, Igor R.; Tan, Zhong Ming

doi:10.3390/universe4010018

The ABC of Higher-Spin AdS/CFT

Simone Giombi
(
- Princeton U.
)
,
Igor R. Klebanov
(
- Princeton U. and
- Princeton U., CTP
)
,
Zhong Ming Tan
(
- Princeton U. and
- Ecole Normale Supérieure, Paris
)

Aug 26, 2016

64 pages

Published in:

Universe 4 (2018) 1, 18

Published: Jan 19, 2018

e-Print:

1608.07611 [hep-th]

DOI:

10.3390/universe4010018

Report number:

PUPT-2505

View in:

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Abstract: (MDPI)

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.

Note:

64 pages

AdS/CFT correspondence
Higher-Spin Symmetry
1/N expansion
field theory: conformal
fermion: Dirac
spin: high
free energy
coupling constant
singlet
AdS/CFT correspondence

References(68)

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