Abstract
We study the higher-spin gauge theory in six-dimensional anti-de Sitter space AdS6 that is based on the exceptional Lie superalgebra F (4). The relevant higher-spin algebra was constructed in arXiv:1409.2185. We determine the spectrum of the theory and show that it contains the physical fields of the Romans F (4) gauged supergravity. The full spectrum consists of an infinite tower of unitary supermultiplets of F (4) which extend the Romans multiplet to higher spins plus a single short supermultiplet.
Motivated by applications to this novel supersymmetric higher-spin theory as well as to other theories, we extend the known one-loop tests of AdS/CFT duality in various directions. The spectral zeta-function is derived for the most general case of fermionic and mixed-symmetry fields, which allows one to test the Type-A and B theories and supersymmetric extensions thereof in any dimension. We also study higher-spin doubletons and partially-massless fields. While most of the tests are successfully passed, the Type-B theory in all even dimensional anti-de Sitter spacetimes presents an interesting puzzle: the free energy as computed from the bulk is not equal to that of the free fermion on the CFT side, though there is some systematics to the discrepancy.
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Günaydin, M., Skvortsov, E. & Tran, T. Exceptional F (4) higher-spin theory in AdS6 at one-loop and other tests of duality. J. High Energ. Phys. 2016, 168 (2016). https://doi.org/10.1007/JHEP11(2016)168
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DOI: https://doi.org/10.1007/JHEP11(2016)168