The Generalized Curvature and Christoffel Symbols for a Higher Spin Potential in AdS_{d+1} Space

Abstract

The generalized curvature tensor and Christoffel symbols are determined in AdS_{d+1} background by a modified ansatz of the de Wit - Freedman type by imposing gauge invariance. The resulting set of recurrence relations and difference equations is solved. The Riemann curvature tensor is derived by antisymmetrization. All results are presented as finite power series in the inverse AdS radius and are unique. The fourth order, which is complete for fields up to spin five, is calculated explicitly. Higher orders can be obtained with the same method.

arXiv comment19 pages, Latex, v2 references added, v3 one section and references added

References in corpus (6)

• AdS Dual of the Critical O(N) Vector Model
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Higher-Spin Gauge Theories in Four, Three and Two Dimensions
• Nonlinear higher spin theories in various dimensions
• The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of $Ad{S}_4$
• The structure of the trace anomaly of higher spin conformal currents in the bulk of $Ad{S}_4$

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• On the relation between local and geometric Lagrangians for higher spins
• New Unfolded Higher Spin Systems in $Ad{S}_3$
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ II: Potentials
• Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models
• On Nonlinear Higher Spin Curvature
• Geometry and dynamics of higher-spin frame fields
• Generalized Curvature and Ricci Tensors for a Higher Spin Potential and the Trace Anomaly in External Higher Spin Fields in AdS_{4} Space
• On special quartic interaction of higher spin gauge fields with scalars and gauge symmetry commutator in the linear approximation
• Restrictions for $n$-Point Vertices in Higher-Spin Theories
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• Covariant Graviton Propagator in Anti-de Sitter Spacetime
• Hierarchy of Supersymmetric Higher Spin Connections
• Local Interactions of Higher-Spin Potentials That are Gauge Invariant in Linear Approximation