Holographic calculations of Rényi entropy

By Ling-Yan Hung, R. Myers, M. Smolkin, A. Yale. 2011

340 citations recorded by the source corpus.

A bstractWe extend the approach of [12] to a new calculation of the Rényi entropy of a general CFT in d dimensions with a spherical entangling surface, in terms of certain thermal partition functions. We apply this approach to calculate the Rényi entropy in various holographic models. Our results indicate that in general, the Rényi entropy will be a complicated nonlinear function of the central charges and other parameters which characterize the CFT. We also exhibit the relation between this new thermal calculation and a conventional calculation of the Rényi entropy where a twist operator is inserted on the spherical entangling surface. The latter insight also allows us to calculate the scaling dimension of the twist operators in the holographic models.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/984aab94f20968b4baf8779d615e43310b4ca6a9

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Citations in the corpus

Entanglement entropy from a holographic viewpoint (2012, methodology): “This analysis has been generalized to calculate the Renyi entropy [55] (see also[56, 57]).”
Relative entropy and holography (2013, methodology): “Unfortunately, progress towards understanding holographic Rényi entropies has been more limited [18, 25, 26].”
Nonlinear gravity from entanglement in conformal field theories (2017, background): “where the first equality defines C̃T in terms of the stress tensor two-point normalization CT (using the convention of [23]).”
Comments on holographic entanglement entropy and RG flows (2012, background): “Here, as in [69], we have normalized CT so that in the limit λ → 0, CT = a ∗ d.”
Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects (2013, methodology): “Moreover, the difference in the free energy of the black brane at temperatures 1/(2πR) and 1/(2πRq) gives the Rényi entropies Sq [28].”
Deriving covariant holographic entanglement (2016, methodology): “In the absence of the scalar term, the calculation will be that of [38].”
Generalized entropy and higher derivative gravity (2013, neutral): “4) [17, 18].”
The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT (2013, methodology): “This breakdown was discussed and confronted in [42] in a similar computation of EREs.”
Causal holographic information (2012, methodology): “, for ∂A = Sd−2 ⊂ Rd−1 = ΣB by using a conformal transformation to map the reduced density matrix to a thermal density matrix and finally computing the latter using black hole entropy as is standard in AdS/CFT (Renyi entropies were computed using this trick in [9]).”
Holographic entanglement beyond classical gravity (2013, neutral): “[15, 9, 16, 5].”
Entanglement entropy: Holography and renormalization group (2018, neutral): “(59) are rewritten in more concise forms (Hung et al., 2011b; Nakaguchi and Nishioka, 2016): S̃(β) ≥ 0 , E(β) ≥ 0 , C(β) ≥ 0 .”
Mutual information and the F-theorem (2015, background): “Now as above, the calculation of the entanglement entropy of this exterior region can again be related to a calculation of thermal entropy in the same space H2 × R [62, 68].”
Entanglement temperature and entanglement entropy of excited states (2013, background): “16) Then, defining complex coordinates σ = u+ i sl and w = r + it on the respective two dimensional slices, we consider the mapping introduced in [23] e−σ = l − w l + w .”