Generalized Curvature and Ricci Tensors for a Higher Spin Potential and the Trace Anomaly in External Higher Spin Fields in AdS_{4} Space

Abstract

The curvature of a higher spin potential as constructed in a previous article of the same authors arXiv:0705.3528 is applied to the analysis of the linearized trace anomaly obtained from the quadratic part of the effective action for a conformally coupled scalar with linearized interaction with the external higher spin fields arXiv:hep-th/0602067. The spin is restricted to four to profit from technical simplifications but without reducing the problem in principle. The issue includes the calculation of all Ricci tensors as multiple traces of the curvature, the derivation of all primary and secondary Bianchi identities, expressing all Ricci tensors as differential operators applied to the Fronsdal term, calculating the Weyl variation of these, and showing finally that Weyl variations of integrals over contracted squares of Ricci tensors can be used to eliminate the anomaly completely. This peculiarity is discussed in detail. As tools we use the formalism of bisymmetric tensor fields whose space is equipped with a local bilinear invariant form, the *-form.

arXiv comment15 pages, Latex,v.2 reference added

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• Direct construction of a cubic selfinteraction for higher spin gauge fields
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
• Off-shell construction of some trilinear higher spin gauge field interactions
• Conformal invariant interaction of a scalar field with the higher spin field in AdS_{D}
• Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models
• On Nonlinear Higher Spin Curvature
• On special quartic interaction of higher spin gauge fields with scalars and gauge symmetry commutator in the linear approximation
• Covariant Graviton Propagator in Anti-de Sitter Spacetime
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians