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Exact results for five-dimensional superconformal field theories with gravity duals,” arXiv:1207.4359 [hep-th
"... We apply the technique of supersymmetric localization to exactly compute the S5 par-tition function of several large N superconformal field theories in five dimensions that have AdS6 duals in massive type IIA supergravity. The localization computations are performed in the non-renormalizable effecti ..."
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We apply the technique of supersymmetric localization to exactly compute the S5 par-tition function of several large N superconformal field theories in five dimensions that have AdS6 duals in massive type IIA supergravity. The localization computations are performed in the non-renormalizable effective field theories obtained through relevant deformations of the UV superconformal field theories. We compare the S5 free energy to a holographic compu-tation of entanglement entropy in the AdS6 duals and find perfect agreement. In particular, we reproduce the N5/2 scaling of the S5 free energy that was expected from supergravity.
Some Calculable Contributions to Holographic Entanglement Entropy
- JHEP
, 2011
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Entanglement entropy in higher derivative holography
, 2013
"... We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena [1] have provided a method to derive the equations for the entangling surface from first principles. We use this method to compute the entangling surface in four derivative gravity. C ..."
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Cited by 22 (4 self)
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We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena [1] have provided a method to derive the equations for the entangling surface from first principles. We use this method to compute the entangling surface in four derivative gravity. Certain interesting differences compared to the two derivative case are pointed out. For Gauss-Bonnet gravity, we show that in the regime where this method is applicable, the resulting equations coincide with proposals in the literature as well as with what follows from considerations of the stress tensor on the entangling surface. Finally we demonstrate that the area functional in Gauss-Bonnet holography arises as a counterterm needed to make the Euclidean action free of power law divergences.
Holographic evolution of the mutual information
, 2011
"... We compute the time evolution of the mutual information in out of equilibrium quantum systems whose gravity duals are Vaidya spacetimes in three and four dimensions, which describe the formation of a black hole through the collapse of null dust. We find the holographic mutual information to be non m ..."
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Cited by 20 (0 self)
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We compute the time evolution of the mutual information in out of equilibrium quantum systems whose gravity duals are Vaidya spacetimes in three and four dimensions, which describe the formation of a black hole through the collapse of null dust. We find the holographic mutual information to be non monotonic in time and always monogamous in the ranges explored. We also find that there is a region in the configuration space where it vanishes at all times. We show that the null energy condition is a necessary condition for both the strong subadditivity of the holographic entanglement entropy and the monogamy of the holographic mutual information.
F-Theorem without Supersymmetry
, 2011
"... The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with N = 2 supersymmetry ..."
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Cited by 17 (2 self)
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The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with N = 2 supersymmetry. In this paper we perform more general tests that do not rely on supersymmetry. We study perturbatively the RG flows produced by weakly relevant operators and show that the free energy decreases monotonically. We also consider large N field theories perturbed by relevant double trace operators, free massive field theories, and some Chern-Simons gauge theories. In all cases the free energy in the IR is smaller than in the UV, consistent with the F-theorem. We discuss other odd-dimensional Euclidean theories on Sd and provide evidence that (−1)(d−1)/2 log |Z | decreases along RG flow; in the particular case d = 1 this is the well-known g-theorem.
Rényi Entropies for Free Field Theories
"... Rényi entropies Sq are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q ≥ 0. For (d + 1)-dimensional conformal field theories, the Rényi entropies across Sd−1 may be extracted from the thermal partition functions of ..."
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Cited by 16 (2 self)
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Rényi entropies Sq are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q ≥ 0. For (d + 1)-dimensional conformal field theories, the Rényi entropies across Sd−1 may be extracted from the thermal partition functions of these theories on either (d+1)-dimensional de Sitter space or R×Hd, where Hd is the d-dimensional hyperbolic space. These thermal partition functions can in turn be expressed as path integrals on branched coverings of the (d+ 1)-dimensional sphere and S1 × Hd, respectively. We calculate the Rényi entropies of free massless scalars and fermions in d = 2, and show how using zeta-function regularization one finds agreement between the calculations on the branched coverings of S3 and on S1 × H2. Analogous calculations for massive free fields provide monotonic interpolating functions between the Rényi entropies at the Gaussian and the trivial fixed points. Finally, we discuss similar Rényi entropy calculations in d> 2.
