Scale Vs. Conformal Invariance in the AdS/CFT Correspondence

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.

4 pages, RevTeX (v3: references added)

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Cited by in corpus (16)

• General (Anti-)de Sitter Black Holes in Five Dimensions
• Rotating AdS black holes in Maxwell-$f(T)$ gravity
• Higher Dimensional Kerr-AdS Black Holes and the AdS/CFT Correspondence
• Reissner-Nordstrom-de Sitter black hole, planar coordinates and dS/CFT
• New rotating black holes in non-linear Maxwell $f(\mathcal{R})$ gravity
• Scale without Conformal Invariance: Theoretical Foundations
• Scale without Conformal Invariance at Three Loops
• Cardy-Verlinde Formula and entropy bounds in Kerr-Newman-AdS${}_4$/dS${}_4$ black holes backgrounds
• Half-Supersymmetric Solutions in Five-Dimensional Supergravity
• Rotating charged AdS solutions in quadratic $f(T)$ gravity
• Discrete scale invariance in holography revisited
• A New Boundary Counterterm for Asymptotically AdS Spacetimes
• First Law, Counterterms and Kerr-AdS_5 Black Holes
• Thermodynamics of 5D Charged Rotating Black Holes: A Counterterms Treatment
• Brane Splitting via Quantum Tunneling
• Scale without Conformal Invariance in bottom-up Holography