Seeing a c-theorem with holography

By R. Myers, Aninda Sinha. 2010

512 citations recorded by the source corpus.

Using the anti-de Sitter conformal theory correspondence, we examine holographic renormalization group flows in a framework where the bulk gravity contains higher curvature interactions. This holographic model allows us to distinguish the flow of the different central charges in dual theory. For example, in four dimensions, one finds that the flow of the central charge a is naturally monotonic but that of c is not. Our results agree with Cardy's proposal to extend Zamolodchikov's c-theorem to higher dimensions. We are also led to formulate a novel c-theorem for a universal coefficient appearing in the entanglement entropy of the fixed point conformal theories in any (including an odd) number of dimensions.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/430193dabc1f821ade6e8d2166599203b06df2ea

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. R. Myers
2. T. Takayanagi
3. T. Nishioka
4. T. Faulkner
5. Ling-Yan Hung
6. V. Hubeny
7. Aninda Sinha
8. M. Smolkin

In Nuclear and High Energy Physics

1. R. Myers
2. T. Takayanagi
3. T. Nishioka
4. T. Faulkner
5. V. Hubeny
6. H. Casini
7. A. Singh
8. M. Rangamani

In Statistical and Nonlinear Physics

1. R. Myers
2. T. Takayanagi
3. T. Nishioka
4. Ling-Yan Hung
5. T. Faulkner
6. M. Smolkin
7. Aninda Sinha
8. A. Singh

Citations in the corpus

• Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects (2013, background): “RT’s proposal has been applied to study various questions and conjectures about EE, including whether EE can count of degrees of freedom in arbitrary d [12, 13].”
• Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere (2011, background): “(2)A seemingly different measure of the number of degrees of freedom in a 3-d CFT was proposed in [12,13]; it is the entanglement entropy between the two hemispheres in the CFT on R × S(2).”
• Averaged null energy condition from causality (2016, background): “Another tantalizing hint is that in holographic theories, RG monotonicity theorems in general dimensions are equivalent to causality in the emergent radial direction [29, 30].”
• Comments on holographic entanglement entropy and RG flows (2012, methodology): “We begin by constructing two flow functions [33, 34]:”
• On the architecture of spacetime geometry (2012, background): “See the discussion around footnote 15 in [21].”
• Entanglement entropy: Holography and renormalization group (2018, background): “They certainly deserve further investigations regardless of their applications to proving the conjectures for the higher-dimensional C-theorem (Giombi and Klebanov, 2015; Klebanov et al., 2011; Myers and Sinha, 2010, 2011).”
• Entanglement entropy from a holographic viewpoint (2012, background): “In the higher dimensional cases, the agreement of q between the AdSd+2 and CFTd+1 has been confirmed in [7, 58, 59, 54] (see also [60–62]).”
• Holographic entanglement entropy in Lovelock gravities (2011, background): “Recently Myers and Sinha [9, 10] have shown that one can formulate an a-theorem in certain higher derivative theories of gravity, but it is not completely clear what the field theoretic counterpart of the corresponding a-function is.”
• Nonlinear gravity from entanglement in conformal field theories (2017, background): “The relation between the usual central charge c and the stress-tensor two-point function normalization is CT = (40/π (4))c for d = 4 (see, for example [19]).”
• Holographic Quantum Critical Transport without Self-Duality (2010, background): “Recently the utility of this approach has been shown in holographic investigations with various higher curvature gravity theories – see, for example, [25, 29, 30, 31, 32].”
• Some calculable contributions to holographic entanglement entropy (2011, background): “In fact, this result can be calculated for any CFT without any reference to holography and it is known that the pre-factor is precisely (−) d2−14A [8, 23, 9, 7] where the A is the central charge appearing in the A-type trace anomaly [24].”
• Black holes in quasi-topological gravity (2010, background): “We make precise the mapping between the gravitational couplings and the dual CFT parameters, as well as exploring other holographic aspects of quasi-topological gravity in [10, 33].”
• On the new massive gravity and AdS/CFT (2010, background): “9) is actually independent of r! In the context of the observation in [12] this is particularly interesting since there a similar expression evaluated at the boundary is related to a central charge.”