c-theorem of the entanglement entropy

Park, Chanyong; Ro, Daeho; Lee, Jung Hun

doi:10.1007/jhep11(2018)165

Cited by 17 publications

(11 citation statements)

References 77 publications

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“…Indeed the holographic entropic c-function has been shown to obey the c-theorem for Lorentz invariant QFT [12,13]. Interesting studies along this direction on RG flows include also [14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

c -theorem for anisotropic RG flows from holographic entanglement entropy

Chu

Giataganas

2020

Phys. Rev. D

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We propose a candidate c-function in arbitrary dimensional quantum field theories with broken Lorentz and rotational symmetry. For holographic theories we derive the necessary and sufficient conditions on the geometric background for these c-functions to satisfy the ctheorem. We obtain the null energy conditions for anisotropic background to show that do not themselves assure the c-theorem. By employing them, we find that is possible to impose conditions on the UV data that are enough to guarantee at least one monotonic c-function along the RG flow. These UV conditions can be used as building blocks for the construction of anisotropic monotonic RG flows. Finally, we apply our results to several known anisotropic theories and identify the region in the parameters space of the metric where the c-theorem holds for our proposed c-function. arXiv:1906.09620v1 [hep-th]

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Section: Introductionmentioning

confidence: 99%

c -theorem for anisotropic RG flows from holographic entanglement entropy

Chu

Giataganas

2020

Phys. Rev. D

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“…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

J. High Energ. Phys.

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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.

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“…We find the non-monotonicity of c-functions in the string frame, that is related JHEP07(2020)043 to dynamics of the dilaton field in UV in our model. There are several proposals in the literature how to define the holographic c-function in the anisotropic backgrounds [100][101][102][103][104][105][106][107].…”

Section: Jhep07(2020)043mentioning

confidence: 99%

Holographic entanglement entropy in anisotropic background with confinement-deconfinement phase transition

Aref’eva

Patrushev

Slepov

2020

J. High Energ. Phys.

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We discuss a general five-dimensional completely anisotropic holographic model with three different spatial scale factors, characterized by a Van der Waals-like phase transition between small and large black holes. A peculiar feature of the model is the relation between anisotropy of the background and anisotropy of the colliding heavy ions geometry. We calculate the holographic entanglement entropy (HEE) of the slab-shaped region, the orientation of which relatively to the beams line and the impact parameter is characterized by the Euler angles. We study the dependences of the HEE and its density on the thermodynamic (temperature, chemical potential) and geometric (parameters of anisotropy, thickness, and orientation of entangled regions) parameters. As a particular case the model with two equal transversal scaling factors is considered. This model is supported by the dilaton and two Maxwell fields. In this case we discuss the HEE and its density in detail: interesting features of this model are jumps of the entanglement entropy and its density near the line of the small/large black hole phase transition. These jumps depend on the anisotropy parameter, chemical potential, and orientation. We also discuss different definitions and behavior of c-functions in this model. The c-function calculated in the Einstein frame decreases while is increasing for all in the isotropic case (in regions of (µ, T )-plane far away from the line of the phase transition). We find the non-monotonicity of the c-functions for several anisotropic configurations, which however does not contradict with any of the existing c-theorems since they all are based on Lorentz invariance.

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c-theorem of the entanglement entropy

Cited by 17 publications

References 77 publications

c -theorem for anisotropic RG flows from holographic entanglement entropy

c -theorem for anisotropic RG flows from holographic entanglement entropy

Holographic anisotropic background with confinement-deconfinement phase transition

Holographic entanglement entropy in anisotropic background with confinement-deconfinement phase transition

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