Holographic c-theorems in arbitrary dimensions

By R. Myers, Aninda Sinha. 2010

687 citations recorded by the source corpus.

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flows is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT’s. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy’s proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.

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

View Paper: https://www.semanticscholar.org/paper/9eb119469ef03b57d8b380ae3924010ada11f379

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. V. Hubeny
4. T. Nishioka
5. M. Rangamani
6. T. Faulkner
7. J. Maldacena
8. D. Stanford

In Nuclear and High Energy Physics

1. R. Myers
2. T. Takayanagi
3. T. Nishioka
4. V. Hubeny
5. J. Maldacena
6. Thomas Hartman
7. M. Rangamani
8. D. Harlow

In Statistical and Nonlinear Physics

1. R. Myers
2. T. Takayanagi
3. V. Hubeny
4. T. Nishioka
5. D. Harlow
6. M. Rangamani
7. D. Stanford
8. T. Faulkner

Citations in the corpus

• Holographic calculations of Rényi entropy (2011, background): “on was chosen so that Ce T = a∗ d in the limit λ → 0. This choice is slightly different from that in [33], i.e.,CT = d+1 d−1 Γ(d+1) πd Ce T . – 13 – the second central charge, we use that identified in [21] as satisfying an interesting holographic c-theorem: a∗ d = πd/2 Γ(d/2) L˜ ℓ P !d−1 1− 2 d− 1 d”
• Some calculable contributions to holographic entanglement entropy (2011, methodology): “As is well known, with even d, EE in a CFT can be directly calculated using the trace anomaly, at least for geometries with sufficient symmetry [3, 8, 6, 9].”
• Black holes and the butterfly effect (2013, background): “In conformal quantum field theories (CFTs) defined on a sphere, the entropy of entanglement between hemispheres of the vacuum state has been shown to be the correct measure of the number of degrees of freedom which decreases under renormalization group flow, encompassing the c, a and F theorems [2, ”
• Comments on holographic entanglement entropy and RG flows (2012, methodology): “We begin by constructing two flow functions [33, 34]:”
• On renormalization group flows in four dimensions (2011, background): “See also the recent illuminating study in [17].”
• Holographic Quantum Critical Transport without Self-Duality (2010, background): “of motion for the gauge field and so, as explained in detail in [33], the dual CFT will contain nonunitary operators.”
• On renormalization group flows and the a-theorem in 6d (2012, methodology): “For even d, this new central charge was shown to precisely match the coefficient of the Euler trace anomaly [8].”
• Holographic evolution of the mutual information (2011, methodology): “This inequality has been employed to study the c theorems from the holographic point of view [45, 46] and their generalizations in presence of boundaries [47, 48, 49, 50].”
• 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.”
• Towards a derivation of holographic entanglement entropy (2011, background): “The (dimensionless) constant ad is a central charge that characterizes the number of degrees of freedom in the boundary CFT [14].”
• 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].”
• Mutual information and the F-theorem (2015, background): “The F -theorem was originally discovered in a holographic framework [11, 12].”
• Entanglement Entropy of Black Holes (2011, background): “The result (299), as is shown in [39, 181], generalizes to a spherical entangling surface in a conformally-flat spacetime of any even dimension.”