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.
Highlights
The importance of flat spacetime conformal field theories (CFT) in theoretical physics can be hardly exaggerated
The present paper aims to generalize this whole setup of conformal field theories to a particular instance of curved spacetimes, namely to conformally flat (CF) spacetimes
When the spacetime is such that there exists a nonvanishing set of conformal Killing vectors (CKV), there is another definition, which coincides with a function of the former in flat spacetime as well as in spacetimes of constant curvature
Summary
The importance of flat spacetime conformal field theories (CFT) in theoretical physics can be hardly exaggerated (cf. for example, [1,2]). They are fixed points of the renormalization group, and as such, they are in some sense, the simplest of all quantum field theories. III, we discuss a new concept of distance, which related to the geodesic distance (Synge’s world function) is not identical to it This distance, dubbed by us as conformal distance, transforms covariantly under all conformal isometries of the CF space, and gets a very simple expression in the natural coordinate system. We end up with our conclusions and suggestions for future work
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
