AdS/CFT in Fractional Dimension and Higher Spin Gravity at One Loop

Abstract

Large-$N$, $\epsilon$-expansion or the conformal bootstrap allow one to make sense of some of conformal field theories in non-integer dimension, which suggests that AdS/CFT may also extend to fractional dimensions. It was shown recently that the sphere free energy and the $a$-anomaly coefficient of the free scalar field can be reproduced as a one-loop effect in the dual higher-spin theory in a number of integer dimensions. We extend this result to all integer and also to fractional dimensions. Upon changing the boundary conditions in the higher-spin theory the sphere free energy of the large-$N$ Wilson-Fisher CFT can also be reproduced from the higher-spin side.

arXiv comment25 pages, one figure; a typo fixed, refs added

References in corpus (26)

• Towards a derivation of holographic entanglement entropy
• AdS Dual of the Critical O(N) Vector Model
• On Renormalization Group Flows in Four Dimensions
• Massless Higher Spins and Holography
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• On the RG running of the entanglement entropy of a circle
• Seeing a c-theorem with holography
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• A universal result on central charges in the presence of double-trace deformations
• One Loop Tests of Higher Spin AdS/CFT
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Partition functions and double-trace deformations in AdS/CFT
• Higher Spin AdS${}_{d+1}$/CFT${}_d$ at One Loop
• Partition function of free conformal higher spin theory
• Notes on Spinning Operators in Fermionic CFT
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Exceptional F(4) Higher-Spin Theory in AdS(6) at One-Loop and other Tests of Duality
• Evolution equations beyond one loop from conformal symmetry
• Double-trace deformations, holography and the c-conjecture
• One-loop Test of Free SU(N) Adjoint Model Holography
• On the Holography of Free Yang-Mills
• Higher spin currents in the critical $O(N)$ vector model at $1/N^2$
• Critical scaling in the large-$N$ $O(N)$ model in higher dimensions and its possible connection to quantum gravity

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• More on Quantum Chiral Higher Spin Gravity
• Type-B Formal Higher Spin Gravity
• AdS one-loop partition functions from bulk and edge characters
• On one loop corrections in higher spin gravity
• Higher Spin Gravities and Presymplectic AKSZ Models
• Off-shell higher-spin fields in $Ad{S}_4$ and external currents
• Partition functions of $p$-forms from Harish-Chandra characters