Iterating free-field AdS/CFT: higher spin partition function relations

Abstract

We find a simple relation between a free higher spin field partition function on thermal quotient of AdS(d+1) and the partition function of the associated d-dimensional conformal higher spin field on thermal quotient of AdS(d). Starting with a conformal higher spin field defined on AdS(d) one may also associate to it another conformal field in d-1 dimensions, thus "iterating" AdS/CFT. We observe that in the case of d=4 this iteration leads to a "trivial" 3d higher spin conformal theory with parity-even non-local action: it describes zero total number of dynamical degrees of freedom and the corresponding partition function on thermal AdS(3) is equal to 1.

27 pages, v2: minor typos corrected

References in corpus (12)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Setting the boundary free in AdS/CFT
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Partition function of free conformal higher spin theory
• Conformal field theories in anti-de Sitter space
• Notes on conformal invariance of gauge fields
• On Dimensional Degression in AdS(d)
• Holographic CFTs on maximally symmetric spaces: correlators, integral transforms and applications
• Saturating the unitarity bound in AdS/CFT_(AdS)
• Aspects of topologically gauged M2-branes with six supersymmetries: towards a "sequential AdS/CFT"?
• Conformal gravity 1-loop partition function
• One loop partition function of six dimensional conformal gravity using heat kernel on AdS

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• On one loop corrections in higher spin gravity
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• A Note on Vectorial AdS${}_5$/CFT${}_4$ Duality for Spin-$j$ Boundary Theory
• One-Loop Free Energy of Tensionless Type IIB String in AdS${}_5\times$S${}^5$
• Unfolded Dynamics Approach and Quantum Field Theory
• Superconformal index of higher derivative $\mathcal{N}=1$ multiplets in four dimensions
• One loop partition function of six dimensional conformal gravity using heat kernel on AdS
• One-loop divergences in 7D Einstein and 6D Conformal Gravities