6d conformal gravity

Abstract

In the framework of ordinary-derivative approach, conformal gravity in space-time of dimension six is studied. The field content, in addition to conformal graviton field, includes two auxiliary rank-2 symmetric tensor fields, two Stueckelberg vector fields and one Stueckelberg scalar field. Gauge invariant Lagrangian with conventional kinetic terms and the corresponding gauge transformations are obtained. One of the rank-2 tensor fields and the scalar field have canonical conformal dimension. With respect to these fields, the Lagrangian contains, in addition to other terms, a cubic potential. Gauging away the Stueckelberg fields and excluding the auxiliary fields via equations of motion, the higher-derivative Lagrangian of 6d conformal gravity is obtained. The higher derivative Lagrangian involves quadratic and cubic curvature terms. This higher-derivative Lagrangian coincides with the simplest Weyl invariant density discussed in the earlier literature. Generalization of de Donder gauge conditions to 6d conformal fields is also obtained.

31 pages, LaTeX-2e, v3: Footnotes 8,9,13, clarifying remark below Eq.(2.30), and references added. Misprints corrected

References in corpus (18)

• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
• Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
• On massive spin 2 interactions
• Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space
• Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: II. Oscillator Realization
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra
• Shadows, currents and AdS fields
• General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
• Gravitational and higher-derivative interactions of massive spin 5/2 field in (A)dS space
• Higher Spins and Open Strings: Quartic Interactions
• Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics
• CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge
• Gravitational Couplings of Higher Spins from String Theory

Cited by in corpus (16)

• Conformal Gravity and Extensions of Critical Gravity
• Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory
• Weyl anomaly of conformal higher spins on six-sphere
• Arbitrary spin conformal fields in (A)dS
• Black Holes in Six-dimensional Conformal Gravity
• Einstein Gravity from Conformal Gravity in 6D
• Anomalous conformal currents, shadow fields and massive AdS fields
• Noncritical Einstein-Weyl Gravity and the AdS/CFT Correspondence
• Not Conformally-Einstein Metrics in Conformal Gravity
• Integration of trace anomaly in 6D
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering
• Almost universal spacetimes in higher-order gravity theories
• Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities
• AdS/BCFT Correspondence for Higher Curvature Gravity: An Example
• Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants
• Anomaly-induced vacuum effective action with torsion: covariant solution and ambiguities