The generalized curvature and Christoffel symbols for a higher spin potential in AdSd+1 space

2007/05/31 by Ruben Manvelyan, Werner Ruehl, W. Rühl · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2007.10.012

published as Nucl.Phys.B797:371-394,2008 · 19 pages, Latex, v2 references added, v3 one section and references added

arxiv created 2007/08/03 · openalex publication_date 2007/10/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Nonlinear higher spin theories in various dimensions
• Tables of Integrals, Series, and Products

Cited by

• Generalized curvature and Ricci tensors for a higher spin potential and the trace anomaly in external higher spin fields in AdS4 space
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization