On the Universal Pieces of Holographic Entanglement Entropy and Holographic Subregion Complexity (original) (raw)
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Universal pieces of holographic entanglement entropy and holographic subregion complexity
Physical Review D, 2020
We propose that the definition of holographic subregion complexity (HSC) needs a slight modification for supergravity solutions with warped anti-de Sitter (AdS) factors. Such warp factors can arise due to the nontrivial dilaton profile, for example, in AdS 6 solutions of type IIA supergravity. This modified definition ensures that the universal piece of the HSC is proportional to that of the holographic entanglement entropy, as is the case for supergravity solutions without warp factors. This also means that the leading behaviour at large N is the same for both these quantities, as we show for some well-known supergravity solutions (with and without warp factors) in various dimensions. We also show that this relation between the universal pieces suggests "universal" relations between field theoretical analogue of HSC and the sphere partition function or Weyl a-anomaly in odd or even dimensions, respectively.
2019
We compute and provide formulae as functions of spacetime dimension for the change in holographic entanglement entropy and subregion complexity of spherical boundary subregions in the AdS black hole background up to third order in the black hole mass. We also compute exact numerical expressions for the fourth-order change in holographic entanglement entropy. We verify that the first law of entanglement is satisfied up to second order. We observe that the change in entanglement entropy is positive at odd orders and negative at even orders, whereas the change in subregion complexity is negative at odd orders and positive at even orders (except in three spacetime dimensions, where it vanishes identically). We conjecture a relation analogous to the first law of thermodynamics in which entanglement plays the role of heat and complexity plays the role of work. The relation between work and complexity is non-universal and dimension-dependent indicating that there may exist additional infor...
2018
The BPS D3 brane has a non-supersymmetric cousin, called the non-susy D3 brane, which is also a solution of type IIB string theory. The corresponding counterpart of black D3 brane is the ‘black’ non-susy D3 brane and like the BPS D3 brane, it also has a decoupling limit, where the decoupled geometry (in the case we are interested, this is asymptotically AdS5 × S) is the holographic dual of a non-conformal, non-supersymmetric QFT in (3+1)dimensions. In this QFT we compute the entanglement entropy (EE), the complexity and the Fisher information metric holographically using the above mentioned geometry for both the strip type and spherical subsystems. We compare our results with the standard AdS5 black hole (the decoupled geometry of black D3 brane) obtained before (only the EE is known and not the complexity which we calculate in this paper) and find that although the Fefferman-Graham expansion of the metric reproduces the result for the entanglement entropy correctly, it fails to do ...
2018
The BPS D3 brane has a non-supersymmetric cousin, called the non-susy D3 brane, which is also a solution of type IIB string theory. The corresponding counterpart of black D3 brane is the `black' non-susy D3 brane and like the BPS D3 brane, it also has a decoupling limit, where the decoupled geometry (in the case we are interested, this is asymptotically AdS_5 × S^5) is the holographic dual of a non-conformal, non-supersymmetric QFT in (3+1)-dimensions. In this QFT we compute the entanglement entropy (EE), the complexity and the Fisher information metric holographically using the above mentioned geometry for both the strip type and spherical subsystems. We compare our results with the standard AdS_5 black hole (the decoupled geometry of black D3 brane) obtained before (only the EE is known and not the complexity which we calculate in this paper) and find that although the Fefferman-Graham expansion of the metric reproduces the result for the entanglement entropy correctly, it fai...
Holographic entanglement entropy and the internal space
Physical Review D, 2015
We elaborate on the role of extremal surfaces probing the internal space in AdS/CFT. Extremal surfaces in AdS quantify the "geometric" entanglement between different regions in physical space for the dual CFT. This, however, is just one of many ways to split a given system into subsectors, and extremal surfaces in the internal space should similarly quantify entanglement between subsectors of the theory. For the case of AdS 5 ×S 5 , their area was interpreted as entanglement entropy between U(n) and U(m) subsectors of U(n + m) N = 4 SYM. Making this proposal precise is subtle for a number of reasons, the most obvious being that from the bulk one usually has access to gauge-invariant quantities only, while a split into subgroups is inherently gauge variant. We study N = 4 SYM on the Coulomb branch, where some of the issues can be mitigated and the proposal can be sharpened. Continuing back to the original AdS 5 ×S 5 geometry, we obtain a modified proposal, based on the relation of the internal space to the R-symmetry group.
On volumes of subregions in holography and complexity
Journal of High Energy Physics, 2016
The volume of the region inside the bulk Ryu-Takayanagi surface is a codimension-one object, and a natural generalization of holographic complexity to the case of subregions in the boundary QFT. We focus on time-independent geometries, and study the properties of this volume in various circumstances. We derive a formula for computing the volume for a strip entangling surface and a general asymptotically AdS bulk geometry. For an AdS black hole geometry, the volume exhibits non-monotonic behaviour as a function of the size of the entangling region (unlike the behaviour of the entanglement entropy in this setup, which is monotonic). For setups in which the holographic entanglement entropy exhibits transitions in the bulk, such as global AdS black hole, geometries dual to confining theories and disjoint entangling surfaces, the corresponding volume exhibits a discontinuous finite jump at the transition point (and so do the volumes of the corresponding entanglement wedges). We compute this volume discontinuity in several examples. Lastly, we compute the codim-zero volume and the bulk action of the entanglement wedge for the case of a sphere entangling surface and pure AdS geometry.
On holographic entanglement entropy and higher curvature gravity
Journal of High Energy Physics, 2011
We examine holographic entanglement entropy with higher curvature gravity in the bulk. We show that in general Wald's formula for horizon entropy does not yield the correct entanglement entropy. However, for Lovelock gravity, there is an alternate prescription which involves only the intrinsic curvature of the bulk surface. We verify that this prescription correctly reproduces the universal contribution to the entanglement entropy for CFT's in four and six dimensions. We also make further comments on gravitational theories with more general higher curvature interactions.
A note on the extensivity of the holographic entanglement entropy
Journal of High Energy Physics, 2008
We consider situations where the renormalized geometric entropy, as defined by the AdS/CFT ansatz of Ryu and Takayanagi, shows extensive behavior in the volume of the entangled region. In general, any holographic geometry that is 'capped' in the infrared region is a candidate for extensivity provided the growth of minimal surfaces saturates at the capping region, and the induced metric at the 'cap' is non-degenerate. Extensivity is well-known to occur for highly thermalized states. In this note, we show that the holographic ansatz predicts the persistence of the extensivity down to vanishing temperature, for the particular case of conformal field theories in 2 + 1 dimensions with a magnetic field and/or electric charge condensates.
Refined holographic entanglement entropy for the AdS solitons and AdS black holes
Nuclear Physics B, 2013
We consider the refinement of the holographic entanglement entropy for the holographic dual theories to the AdS solitons and AdS black holes, including the corrected ones by the Gauss-Bonnet term. The refinement is obtained by extracting the UV-independent piece of the holographic entanglement entropy, the so-called renormalized entanglement entropy which is independent of the choices of UV cutoff. Our main results are (i) the renormalized entanglement entropies of the AdS d+1 soliton for d = 4, 5 are neither monotonically decreasing along the RG flow nor positive definite, especially around the deconfinement/confinement phase transition; (ii) there is no topological entanglement entropy for AdS 5 soliton even with Gauss-Bonnet correction; (iii) for the AdS black holes, the renormalized entanglement entropy obeys an expected volume law at IR regime, and the transition between UV and IR regimes is a smooth crossover even with Gauss-Bonnet correction; (iv) based on AdS/MERA conjecture, we postulate that the IR fixed-point state for the non-extremal AdS soliton is a trivial product state.
On holographic Rényi entropy in some modified theories of gravity
Journal of High Energy Physics, 2018
We perform a detailed analysis of holographic entanglement Rényi entropy in some modified theories of gravity with four dimensional conformal field theory duals. First, we construct perturbative black hole solutions in a recently proposed model of Einsteinian cubic gravity in five dimensions, and compute the Rényi entropy as well as the scaling dimension of the twist operators in the dual field theory. Consistency of these results are verified from the AdS/CFT correspondence, via a corresponding computation of the Weyl anomaly on the gravity side. Similar analyses are then carried out for three other examples of modified gravity in five dimensions that include a chemical potential, namely Born-Infeld gravity, charged quasi-topological gravity and a class of Weyl corrected gravity theories with a gauge field, with the last example being treated perturbatively. Some interesting bounds in the dual conformal field theory parameters in quasi-topological gravity are pointed out. We also p...