Exceptional F(4) Higher-Spin Theory in AdS(6) at One-Loop and other Tests of Duality

TL;DR

This paper explores a six-dimensional higher-spin gauge theory based on the exceptional Lie superalgebra F(4), analyzing its spectrum, duality tests, and extending one-loop calculations to various fields and dimensions.

Contribution

It constructs and studies the spectrum of the F(4)-based higher-spin theory in AdS6, extending one-loop duality tests to fermionic and mixed-symmetry fields, and investigates discrepancies in Type-B theories.

Findings

Spectrum includes higher-spin supermultiplets extending Romans F(4) supergravity.

Derived spectral zeta-function for fermionic and mixed-symmetry fields.

Identified a discrepancy in free energy calculations for Type-B theories in even dimensions.

Abstract

We study the higher-spin gauge theory in six-dimensional anti-de Sitter space $AdS_6$ that is based on the exceptional Lie superalgebra $F(4)$. The relevant higher-spin algebra was constructed in arXiv:1409.2185 [hep-th]. 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.