CFT in Conformally Flat Spacetimes

Abstract

A new class of conformal field theories is presented, where the background gravitational field is conformally flat. Conformally flat (CF) spacetimes enjoy conformal properties quite similar to the ones of flat spacetime. The conformal isometry group is of maximal rank and the conformal Killing vectors in conformally flat coordinates are {\em exactly} the same as the ones of flat spacetime. In this work, a new concept of distance is introduced, the {\em conformal distance}, which transforms covariantly under all conformal isometries of the CF space. It is shown that precisely for CF spacetimes, an adequate power of the said conformal distance is a solution of the non-minimal d'Alembert equation.

arXiv commentMinor changes and some clarifications added. Published version. 16 pages

References in corpus (6)

• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Correlation Functions of the Energy Momentum Tensor on Spaces of Constant Curvature
• Supersymmetry on curved spaces and superconformal anomalies
• Global Supersymmetry on Curved Spaces in Various Dimensions
• Improved Epstein-Glaser renormalization in $x$-space versus differential renormalization
• Conformal invariance versus Weyl invariance

Cited by in corpus (5)

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• Harvesting Fermionic Field Entanglement in Schwarzschild Spacetime
• Holographic 2-Point Functions in the Pseudo-Conformal Universe
• Effective action in elliptic and hyperbolic spacetimes