An embedding formalism for CFTs in general states on curved backgrounds

Enrico Parisini, Kostas Skenderis, Benjamin Withers

Published 2022-09-19Version 1

We present a generalisation of the embedding space formalism to conformal field theories (CFTs) on non-trivial states and curved backgrounds, based on the ambient metric of Fefferman and Graham. The ambient metric is a Lorentzian Ricci-flat metric in $d+2$ dimensions and replaces the Minkowski metric of the embedding space. It is canonically associated with a $d$-dimensional conformal manifold, which is the physical spacetime where the CFT${}_d$ lives. We propose a construction of CFT${}_d$ correlators in non-trivial states and on curved backgrounds using appropriate geometric invariants of the ambient space as building blocks. As a test of the formalism we apply it to thermal 2-point functions and find exact agreement with a holographic computation and expectations based on thermal operator product expansions (OPEs).