Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT

Abstract

We consider general-symmetry higher spin fields in AdS_5 and derive expressions for their one-loop corrections to vacuum energy E and the associated 4d boundary conformal anomaly a-coefficient. We a propose a similar expression for the second conformal anomaly c-coefficient. We show that all the three quantities (E, a, c) computed for N=8 gauged 5d supergravity are -1/2 of the values for N=4 conformal 4d supergravity and also twice the values for N=4 Maxwell multiplet. This gives 5d derivation of the fact that the system of N=4 conformal supergravity and four N=4 Maxwell multiplets is anomaly free. The values of (E, a, c) for the states at level p of Kaluza-Klein tower of 10d type IIB supergravity compactified on S^5 turn out to be equal to those for p copies of N=4 Maxwell multiplets. This may be related to the fact that these states appear in the tensor product of p superdoubletons. Under a natural regularization of the sum over p, the full 10d supergravity contribution is then minus that of the Maxwell multiplet, in agreement with the standard adjoint AdS/CFT duality (SU(n) SYM contribution is n^2-1 of one Maxwell multiplet). We also verify the matching of (E, a, c) for spin 0 and 1/2 boundary theory cases of vectorial AdS/CFT duality. The consistency conditions for vectorial AdS/CFT turn out to be equivalent to the cancellation of anomalies in the closely related 4d conformal higher spin theories. In addition, we study novel example of vectorial AdS/CFT duality when the boundary theory is described by free spin 1 fields and is dual to a particular higher spin theory in AdS_5 containing fields in mixed-symmetry representations. We also discuss its supersymmetric generalizations.

arXiv comment56 pages. v2,v3: minor corrections, references added

References in corpus (100)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• A Stress Tensor for Anti-de Sitter Gravity
• The Holographic Weyl anomaly
• AdS Dual of the Critical O(N) Vector Model
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Massless Higher Spins and Holography
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• The Hagedorn Transition, Deconfinement and N=4 SYM Theory
• Nonlinear higher spin theories in various dimensions
• Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Stringy gravity, interacting tensionless strings and massless higher spins
• Cubic interaction vertices for massive and massless higher spin fields
• D=4 Super Yang Mills, D=5 gauged supergravity and D=4 conformal supergravity
• On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
• Spinning AdS Propagators
• A universal result on central charges in the presence of double-trace deformations
• On stringy AdS_5 x S^5 and higher spin holography
• Conformal Higher Spin Theory
• One Loop Tests of Higher Spin AdS/CFT
• On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory
• Holography of the N=1 Higher-Spin Theory on AdS4
• Notes On Higher Spin Symmetries
• Cubic Interactions of Bosonic Higher Spin Gauge Fields in $Ad{S}_5$
• Conformal Higher Spin Symmetries of 4d Massless Supermultiplets and $osp(L,2M)$ Invariant Equations in Generalized (Super)Space
• On N=8 Supergravity on $Ad{S}_5$ and N=4 Superconformal Yang-Mills theory
• Effective action in a higher-spin background
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Doubletons and 5D Higher Spin Gauge Theory
• Double-trace operators and one-loop vacuum energy in AdS/CFT
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Partition functions and double-trace deformations in AdS/CFT
• Higher Spin Superalgebras in any Dimension and their Representations
• On partition function and Weyl anomaly of conformal higher spin fields
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• On the Frame-Like Formulation of Mixed-Symmetry Massless Fields in (A)dS(d)
• On limits of superstring in AdS_5 x S^5
• The Heat Kernel on AdS_3 and its Applications
• 4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5
• Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory
• AdS Description of Induced Higher-Spin Gauge Theory
• N=1 Supersymmetric Theory of Higher Spin Gauge Fields in AdS(5) at the Cubic Level
• Elements of Vasiliev theory
• Higher Spin AdS${}_{d+1}$/CFT${}_d$ at One Loop
• Conformal Maxwell theory as a singleton field theory on AdS_5, IIB three-branes and duality
• Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
• Massive totally symmetric fields in AdS(d)
• Towards Massless Higher Spin Extension of D=5, N=8 Gauged Supergravity
• Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime
• Partition function of free conformal higher spin theory
• Novel supermultiplets of SU(2,2|4) and the AdS_5/CFT_4 duality
• Generating functions of (partially-)massless higher-spin cubic interactions
• Conformally Covariant Differential Operators: Properties and Applications
• On the spectrum of AdS/CFT beyond supergravity
• Partition Sums and Entropy Bounds in Weakly Coupled CFT
• Conformal Higher Spin Currents in Any Dimension and AdS/CFT Correspondence
• Singletons, Doubletons and M-theory
• Higher-spin current multiplets in operator-product expansions
• On spin 3 interacting with gravity
• N=4 Superconformal Characters and Partition Functions
• Vector Models in the Singlet Sector at Finite Temperature
• Gravitational cubic interactions for a simple mixed-symmetry gauge field in AdS and flat backgrounds
• FV-type action for AdS(5) mixed-symmetry fields
• Heat kernel asymptotics with mixed boundary conditions
• Fermionic fields in the d-dimensional anti-de Sitter spacetime
• The Heat Kernel on $AdS$
• Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory
• A Note on the Chiral Anomaly in the AdS/CFT Correspondence and 1/N^2 Correction
• Gauge fields as composite boundary excitations
• Conformally Covariant Differential Operators: Symmetric Tensor Fields
• Stress Tensors from Trace Anomalies in Conformal Field Theories
• Higher Spin Conformal Currents in Minkowski Space
• Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons
• On conformal higher spin wave operators
• Antisymmetric tensor field on $Ad{S}_5$
• Weyl anomaly of conformal higher spins on six-sphere
• Partition Functions for Higher-Spin theories in AdS
• Constraining conformal field theory with higher spin symmetry in four dimensions
• Constraining conformal field theories with a higher spin symmetry in d=4
• Towards higher-spin holography in ambient space of any dimension
• Polyakov formulas for GJMS operators from AdS/CFT
• 1/N^2 corrections to the holographic Weyl anomaly
• Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary
• Order 1/N^2 test of the Maldacena conjecture: Cancellation of the one-loop Weyl anomaly
• Mixed-symmetry tensor conserved currents and AdS/CFT correspondence
• Quantum Effective Action in Spacetimes with Branes and Boundaries
• The spectrum of IIB supergravity on AdS_5 x S^5/Z_3 and a 1/N^2 test of AdS/CFT
• The Spectrum of Yang Mills on a Sphere
• The Boundary Weyl Anomaly in the $\mathcal{N}=4$ SYM/Type IIB Supergravity Correspondence
• Gauged Vector Models and Higher-Spin Representations in AdS_5
• Weyl Anomaly Induced Stress Tensors in General Manifolds
• Massless hook field in AdS(d+1) from the holographic perspective
• Casimir energy of confining large $N$ gauge theories
• CFT adapted approach to massless fermionic fields, AdS/CFT, and fermionic conformal fields
• Conformal self-dual fields
• Conformally invariant wave equation for a symmetric second rank tensor ("spin-2") in d-dimensional curved background
• CFT(4) Partition Functions and the Heat Kernel on AdS(5)
• On cubic AdS interactions of mixed-symmetry higher spins

Cited by in corpus (96)

• Loops in AdS from Conformal Field Theory
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• More on Quantum Chiral Higher Spin Gravity
• Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
• Spinning AdS Loop Diagrams: Two Point Functions
• High-temperature asymptotics of supersymmetric partition functions
• 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
• High-Temperature Expansion of Supersymmetric Partition Functions
• On triviality of S-matrix in conformal higher spin theory
• From Higher Spins to Strings: A Primer
• TASI Lectures on the Higher Spin - CFT duality
• On quantum corrections in higher-spin theory in flat space
• AdS Weight Shifting Operators
• AdS${}_5$ Holography and Higher-Derivative Supergravity
• Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations
• One-loop Finiteness of Chiral Higher Spin Gravity
• Cardy Formula for 4d SUSY Theories and Localization
• Positivity, negativity, and entanglement
• Conformal anomaly c-coefficients of superconformal 6d theories
• Interactions in Higher-Spin Gravity: a Holographic Perspective
• $1/N$ expansion of circular Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver
• Scalar scattering via conformal higher spin exchange
• Rotating Higher Spin Partition Functions and Extended BMS Symmetries
• Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations
• One-loop Test of Free SU(N) Adjoint Model Holography
• Origin of inflation in CFT driven cosmology: $R^2$-gravity and non-minimally coupled inflaton models
• Type-B Formal Higher Spin Gravity
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• Central charges from the $\mathcal{N}=1$ superconformal index
• $C_T$ for higher derivative conformal fields and anomalies of (1,0) superconformal 6d theories
• Minimal models of field theories: Chiral Higher Spin Gravity
• On the Holography of Free Yang-Mills
• Partition function of free conformal fields in 3-plet representation
• Feynman rules for higher-spin gauge fields on AdS${}_{d+1}$
• On conformal higher spins in curved background
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• $C_T$ for conformal higher spin fields from partition function on conically deformed sphere
• Exact strong coupling results in $\mathcal{N}$=2 $Sp(2N)$ superconformal gauge theory from localization
• On one loop corrections in higher spin gravity
• Partially Massless Higher-Spin Theory II: One-Loop Effective Actions
• Cubic interactions of arbitrary spin fields in 3d flat space
• Iterating free-field AdS/CFT: higher spin partition function relations
• Free energy and boundary anomalies on ${\mathbb{S}}^a\times {\mathbb{H}}^b$ spaces
• A Stringy theory in three dimensions and Massive Higher Spins
• Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography
• Divergences and Boundary Modes in N=8 Supergravity
• Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT
• Higher Spin Gravities and Presymplectic AKSZ Models
• CFT driven cosmology and conformal higher spin fields
• Perturbative analysis in higher-spin theories
• Planar solutions of higher-spin theory I: free field level
• Simple recipe for holographic Weyl anomaly
• T-Reflection
• Ambitwistors, oscillators and massless fields on $Ad{S}_5$
• Lectures on Higher Spin Holography
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• A Note on Vectorial AdS${}_5$/CFT${}_4$ Duality for Spin-$j$ Boundary Theory
• New type of hill-top inflation
• Quantum Corrections to Central Charges and Supersymmetric Casimir Energy in AdS${}_3$/CFT${}_2$
• AdS/CFT in Fractional Dimension and Higher Spin Gravity at One Loop
• Off-shell higher-spin fields in $Ad{S}_4$ and external currents
• Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all
• One-Loop Free Energy of Tensionless Type IIB String in AdS${}_5\times$S${}^5$
• High-temperature asymptotics of the 4d superconformal index
• On divergences in non-minimal N=4 conformal supergravity
• Unfolded Dynamics Approach and Quantum Field Theory
• Character Integral Representation of Zeta function in AdS${}_{d+1}$: II. Application to partially-massless higher-spin gravities
• On higher spin partition functions
• Character Integral Representation of Zeta function in AdS${}_{d+1}$: I. Derivation of the general formula
• Spectral sum rules for confining large-N theories
• Superconformal index of higher derivative $\mathcal{N}=1$ multiplets in four dimensions
• On the Weyl anomaly of 4D Conformal Higher Spins: a holographic approach
• One-Loop Holographic Weyl Anomaly in Six Dimensions
• One-loop supergravity on ${\mathrm{AdS}}_4\times S^7/{\mathbb{Z}}_k$ and comparison with ABJM theory
• Holographic computation of quantum corrections to the bulk cosmological constant
• BRST-BV approach to massless fields adapted to AdS/CFT correspondence
• Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $Ad{S}_5\times {\mathbb{RP}}^5$
• GJMS-like operators on symmetric 2-tensors and their gravitational duals
• Conformal a-anomaly of some non-unitary 6d superconformal theories
• Symmetries and Invariants in Higher-Spin Theory
• BPS Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)$ "orientifold" gauge theory and weak-strong coupling interpolation
• Central charges, elliptic genera, and Bekenstein-Hawking entropy in $\mathcal{N}=(2,2)$ AdS${}_3$/CFT${}_2$
• Worldsheet Free Fields, Higher Spin Symmetry and Free $\mathcal{N}=4$ Super Yang-Mills
• A study about black hole solutions with nonconstant transversal curvature and its conserved charges in Lovelock gravity
• Casimir energy on the sphere and 6D CFT trace anomaly
• On heat coefficients, multiplicative anomaly and 4D Casimir energy for GJMS operators
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• The Weyl Anomaly from the 6D Superconformal Index
• Exploring Free Matrix CFT Holographies at One-Loop
• Holography, Supergravity, and the Weak Gravity Conjecture
• One-loop divergences in 7D Einstein and 6D Conformal Gravities
• Strong coupling expansion of free energy and BPS Wilson loop in $\mathcal{N}=2$ superconformal models with fundamental hypermultiplets