On the conformal transformation and duality in gravity

TL;DR

This paper explores the extension of conformal duality in gravity theories across various dimensions, analyzing its implications for quantum gravity and deriving gauge-independent results relevant for strong curvature regimes.

Contribution

The paper generalizes conformal duality to arbitrary dimensions and sigma-model scalar theories, and discusses its applications in quantum gravity and gauge independence.

Findings

Derived the trace of the first Schwinger-DeWitt coefficient.

Analyzed gauge-fixing dependence and methods to obtain gauge-independent results.

Explored potential applications in quantum gravity in strong curvature regimes.

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 $n \neq 2$ 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.