Constraints on renormalization group flows from holographic entanglement entropy

We present new anisotropic black brane solutions in 5D Einstein-dilaton-twoMaxwell system. The anisotropic background is specified by an arbitrary dynamical exponent ν, a nontrivial warp factor, a non-zero dilaton field, a non-zero time component of the first Maxwell field and a non-zero longitudinal magnetic component of the second Maxwell field. The blackening function supports the Van der Waals-like phase transition between small and large black holes for a suitable first Maxwell field charge. The isotropic case corresponding to ν = 1 and zero magnetic field reproduces previously known solutions. We investigate the anisotropy influence on the thermodynamic properties of our background, in particular, on the small/large black holes phase transition diagram.We discuss applications of the model to the bottom-up holographic QCD. The RG flow interpolates between the UV section with two suppressed transversal coordinates and the IR section with the suppressed time and longitudinal coordinates due to anisotropic character of our solution. We study the temporal Wilson loops, extended in longitudinal and transversal directions, by calculating the minimal surfaces of the corresponding probing open string world-sheet in anisotropic backgrounds with various temperatures and chemical potentials. We find that dynamical wall locations depend on the orientation of the quark pairs, that gives a crossover transition line between confinement/deconfinement phases in the dual gauge theory. Instability of the background leads to the appearance of the critical points (µ ϑ,b , T ϑ,b ) depending on the orientation ϑ of quark-antiquark pairs in respect to the heavy ions collision line.

Section: )mentioning

confidence: 99%

“…We find the non-monotonicity of cfunctions in the string frame, that is related to dynamics of the dilaton field in UV in our model. There are several proposal in the literature how to define the holographic c-function in the anisotropic backgrounds [90][91][92][93][94][95][96][97]. Here we use prescription [95] adapted to our renormalization schemes.…”

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confidence: 99%

Holographic anisotropic background with confinement-deconfinement phase transition

Aref’eva

Rannu

2018

“…Other interesting developments include the correspondence between bulk locality and quantum error correction [24,25], the quantum Bousso bound [26,27], the RG flow of entanglement entropy [28,29], quantum entanglement of local operators [30], the relation between quantum dimension and entanglement entropy [31] and the holographic three point functions of stress tensor [32].…”

Section: Jhep10(2015)049mentioning

confidence: 99%

Universal terms of entanglement entropy for 6d CFTs

Miao

2015

Abstract:We derive the universal terms of entanglement entropy for 6d CFTs by applying the holographic and the field theoretical approaches, respectively. Our formulas are conformal invariant and agree with the results of [37,38]. Remarkably, we find that the holographic and the field theoretical results match exactly for the C 2 and Ck 2 terms, where C and k denote the Weyl tensor and the extrinsic curvature, respectively. As for the k 4 terms, we meet the splitting problem of the conical metrics. The splitting problem in the bulk can be fixed by equations of motion. As for the splitting on the boundary, we assume the general forms and find that there indeed exists suitable splitting which can make the holographic and the field theoretical k 4 terms match. Since we have much more equations than the free parameters, the match for k 4 terms is non-trivial.

“…It should be mentioned that Camps [20] also made important contributions in this direction. For recent developments of HEE, please refer to [21][22][23][24][25][26][27][28][29][30][31][32]. So far, HEE for gravitational actions which include derivatives of the curvature is not known.…”

Section: Jhep08(2015)031mentioning

confidence: 99%

Holographic entanglement entropy for the most general higher derivative gravity

Miao

Guo

2015

134

The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the 'anomaly of entropy' of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.