Scale Vs. Conformal Invariance in the AdS/CFT Correspondence

TL;DR

This paper demonstrates that certain field theories can be scale invariant without being conformally invariant by analyzing rotating black hole backgrounds in the AdS/CFT correspondence, providing explicit examples and computations.

Contribution

It provides explicit examples of non-trivial scale invariant but non-conformally invariant theories using AdS/CFT and rotating black hole backgrounds.

Findings

Rotation breaks conformal invariance but preserves scale invariance.

Explicit computation of action and stress tensor for theories on rotating Einstein universes.

AdS/CFT serves as a natural framework for generating and analyzing such theories.

Abstract

We present two examples of non-trivial field theories which are scale invariant, but not conformally invariant. This is done by placing certain field theories, which are conformally invariant in flat space, onto curved backgrounds of a specific type. We define this using the AdS/CFT correspondence, which relates the physics of gravity in asymptotically Anti-de Sitter (AdS) spacetimes to that of a conformal field theory (CFT) in one dimension fewer. The AdS rotating (Kerr) black holes in five and seven dimensions provide us with the examples, since by the correspondence we are able to define and compute the action and stress tensor of four and six dimensional field theories residing on rotating Einstein universes, using the ``boundary counterterm'' method. The rotation breaks conformal but not scale invariance. The AdS/CFT framework is therefore a natural arena for generating such examples of non-trivial scale invariant theories which are not conformally invariant.