The structure of the trace anomaly of higher spin conformal currents in the bulk of $Ad{S}_4$

Abstract

The two-point function of the conserved traceless spin-$\ell$ currents which are constructed from the scalar field $\sigma (z)$ is evaluated and renormalized by a dimensional regularization procedure. The anomaly is managed to arise only in the trace part. To isolate this trace anomaly it is sufficient to analyze only the maximum singular part of the two-point function and its trace terms to leading order. The corresponding part of the effective action which is quadratic in the trace of the higher spin field is explicitly given. For the spin-2 field which is identical with the gravitational field the results known from the literature are reproduced.

arXiv commentlatex, 21 pages,v.2 minor addition, ref. added, v.3 accepted in Nucl.Phys. B

References in corpus (18)

• AdS Dual of the Critical O(N) Vector Model
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Twenty Years of the Weyl Anomaly
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Higher-Spin Gauge Theories in Four, Three and Two Dimensions
• Graviton and gauge boson propagators in AdS(d+1)
• Evaluating the AdS dual of the critical O(N) vector model
• Correlation Functions of the Energy Momentum Tensor on Spaces of Constant Curvature
• Diffeomorphisms, Anomalies and the Fefferman-Graham Ambiguity
• The group approach to AdS space propagators
• Conformal Coupling of Higher Spin Gauge Fields to a Scalar Field in $Ad{S}_4$ and Generalized Weyl Invariance
• The group approach to AdS space propagators: A fast algorithm
• The masses of gauge fields in higher spin field theory on AdS(4)
• The masses of gauge fields in higher spin field theory on the bulk of $Ad{S}_4$
• The off-shell behaviour of propagators and the Goldstone field in higher spin gauge theory on $Ad{S}_{d+1}$ space
• The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of $Ad{S}_4$
• Lifting a Conformal Field Theory from D-Dimensional Flat Space to (D+1)-Dimensional Ads Space

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• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
• Conformal invariant interaction of a scalar field with the higher spin field in AdS_{D}
• The Generalized Curvature and Christoffel Symbols for a Higher Spin Potential in AdS_{d+1} Space
• Generalized Curvature and Ricci Tensors for a Higher Spin Potential and the Trace Anomaly in External Higher Spin Fields in AdS_{4} Space
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• Covariant Graviton Propagator in Anti-de Sitter Spacetime
• Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in $d=4$
• Boundary action of free AdS higher-spin gauge fields and the holographic correspondence
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$