On the conformal transformation and duality in gravity

Abstract

The theory described by the sum of the Einstein-Hilbert action and the action of conformal scalar field possesses the duality symmetry which includes some special conformal transformation of the metric, and also inversion of scalar field and of the gravitational constant. In the present paper the conformal duality is generalized for arbitrary space-time dimension $n\ne 2$ and for the general sigma-model type conformal scalar theory. We also consider to apply the conformal duality for the investigation of quantum gravity in the strong curvature regime. The trace of the first coefficient of the Schwinger-DeWitt expansion is derived and it's dependence on the gauge fixing condition is considered. After that we discuss the way to extract the gauge-fixing independent result and also it's possible physical applications.

LaTeX, 15 pages, no figures. To appear in Classical and Quantum Gravity

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Cited by in corpus (7)

• Conformal Transformations with Multiple Scalar Fields
• Conformal symmetry, anomaly and effective action for metric-scalar gravity with torsion
• Renormalization group study of the higher derivative conformal scalar model
• Conformal relativity versus Brans-Dicke and superstring theories
• Conformal Transformations in Metric-Affine Gravity and Ghosts
• Transport in a gravity dual with a varying gravitational coupling constant
• Quantum gravity correction, evolution of scalar field and inflation