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.

19 pages, Latex, v2 references added, v3 one section and references added

References in corpus (1)

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

Cited by in corpus (7)

• Geometric Lagrangians for massive higher-spin fields
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
• 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
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• Hierarchy of Supersymmetric Higher Spin Connections