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.
Highlights
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)
AdS/CFT duality implies the equivalence of M/Superstring theory formulated on the product of anti-de Sitter spacetimes AdSd+1 with some compact manifold and certain superconformal field theories on d-dimensional Minkowskian spacetimes which correspond to the boundaries of AdSd+1 [1,2,3]
The basic properties of higher-spin (HS) AdS/CFT dualities include: (i) higher-spin theories are in most cases duals of CFT’s with matter in fundamental representation rather than in adjoint [5], which simplifies the spectrum of single-trace operators and reduces the field content of HS theories as compared to string theory; (ii) unbroken higher-spin theories are expected to be dual to free CFT’s [5,6,7,8]; (iii) models of HS AdS/CFT dualities exist in any spacetime dimension [8]; (iv) interacting CFT’s, like the Wilson-Fisher O(N ) model, can be duals of the same higher-spin theories for a different choice of boundary conditions [5, 9, 10]; (v) the duals of CFT’s with matter in the adjoint representation
Summary
AdS/CFT duality implies the equivalence of M/Superstring theory formulated on the product of anti-de Sitter spacetimes AdSd+1 with some compact manifold and certain superconformal field theories on d-dimensional Minkowskian spacetimes which correspond to the boundaries of AdSd+1 [1,2,3]. Singletons and doubletons and their supermultiplets play a fundamental role in the construction of the Kaluza-Klein spectra of 11d supergravity [14, 15] and type IIB supergravity [16] and in the formulation of higher-spin theories [4, 8, 17,18,19,20,21,22,23] They are massless conformal fields: scalar, fermion, spin-one in 4d etc. Motivated by our study of the exceptional F (4) higher-spin theory in AdS6 we extend the one-loop tests to a number of cases: (i) we derive the spectral zeta-function for arbitrary mixed-symmetry bosonic and fermionic fields; (ii) we compute one-loop determinants for Type-A and Type-B theories; (iii) we study the contributions of fermionic HS fields in diverse dimensions, which is crucial for the consistency of SUSY HS theories; (iv) in AdS5 we study Type-D,E,.
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