Exceptional F (4) higher-spin theory in AdS₆ at one-loop and other tests of duality

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.