c -theorem for anisotropic RG 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

“…In all the aforementioned cases, the proof of the c-theorem utilizes Lorentz invariance in one way or another. There have been several attempts to find a monotonic c-function valid in holographic models with broken Lorentz invariance, with some partial success [72][73][74][75][76]. As more recently shown in [75], for a theory with an anisotropic scaling symmetry the entanglement entropy of an infinitely extended strip depends on the separation between the two sides with an exponent determined by the scaling exponents and the number of dimensions.…”

Section: Holographic Entanglement Entropy and C-functionsmentioning

confidence: 99%

Holographic spontaneous anisotropy

Hoyos

Jokela

Penín

et al. 2020

We construct a family of holographic duals to anisotropic states in a strongly coupled gauge theory. On the field theory side the anisotropy is generated by giving a vacuum expectation value to a dimension three operator. We obtain our gravity duals by considering the geometry corresponding to the intersection of D3-and D5-branes along 2+1 dimensions. Our backgrounds are supersymmetric and solve the fully backreacted equations of motion of ten-dimensional supergravity with smeared D5-brane sources. In all cases the geometry flows to AdS 5 × S 5 in the UV, signaling an isotropic UV fixed point of the dual field theory. In the IR, depending on the parameters of the solution, we find two possible behaviors: an isotropic fixed point or a geometry with anisotropic Lifshitz-like scaling symmetry. We study several properties of the solutions, including the entanglement entropy of strips. We show that any natural extension of existing c-functions will display non-monotonic behavior, conforming with the presence of new degrees of freedom only at intermediate energy scales. * hoyoscarlos@uniovi.es †

“…From the viewpoint of the boundary theory, this gives a quench on the system at t = 0 and subsequently the system evolves into a thermal equilibrium state. Nevertheless, the null energy conditions (NECs) constrain the parameters in the metric [40], obtained as…”

Section: The Holography Backgroundmentioning

confidence: 99%

Holographic approach to thermalization in general anisotropic theories

Sun

Lee

Yeh

2021

We employ the holographic approach to study the thermalization in the quenched strongly-coupled field theories with very general anisotropic scalings including Lifshitz and hyperscaling violating fixed points. The holographic dual is a Vaidya-like time-dependent geometry where the asymptotic metric has general anisotropic scaling isometries. We find the Ryu-Takanayagi extremal surface and use it to calculate the time-dependent entanglement entropy between a strip region with width 2R and its outside region. In the special case with an isotropic metric, we also explore the entanglement entropy for a spherical region of radius R. The growth of the entanglement entropy characterizes the thermalization rate after a quench. We study the thermalization process in the early times and late times in both large R and small R limits. The allowed scaling parameter regions are constrained by the null energy conditions as well as the condition for the existence of the Ryu-Takanayagi extremal surfaces. This generalizes the previous works on this subject. All obtained results can be compared with experiments and other methods of probing thermalization.