In this note we consider a relativistic heavy quark which moves in the quark-gluon plasmas. By using the holographic methods, we analyze the Langevin diffusion process of this relativistic heavy quark. This heavy quark is described by a trailing string attached to a flavor brane and moving at constant velocity. The fluctuations of this string are related to the thermal correlators and the correlation functions are precisely the kinds of objects that we compute in the gravity dual picture. We obtain the action of the trailing string in hyperscaling violation backgrounds and we then find the equations of motion. These equations lead us to construct the Langevin correlator which helps us to obtain the Langevin constants. Using the Langevin correlators we derive the densities spectral and simple analytic expressions in the small and large frequency limits. We examine our works for planar and $R$-charged black holes with hyperscaling violation and find new constraints on $θ$ in the presence of velocity $v$.
We examine the holographic entanglement entropy in hyperscaling violating backgrounds. Precisely in such theories by semi-analytic computation, we use holographic methods to derive the universal terms of entanglement entropy in various dimensions. We also find such terms when the bulk action includes higher-order curvature terms. We make further comments on the mutual information in hyperscaling violating backgrounds with higher curvature interactions. We explore the sign of tripartite information which results in a monogamy property on mutual information. It is shown that for various hypersca…
In this work, we consider a class of hyperscaling violating Lifshitz-like black branes with metric scaling components $z=2$ and $θ=-1$ whose corresponding holographic model can be treated as a non-relativistic fluid exhibiting Lifshitz-type symmetry. Having performed analytical calculations via the Klein-Gordon equation and the linear response theory, the experimental realizations of the concerned model, namely the transport coefficients, are found to behave as $η\propto T^{3/2}$, $σ_{DC} \propto T^{3/2}$, and $ρ_{DC} \propto T^{-3/2}$. The associated metric scaling exponents from the bulk the…
Revisiting holographic superconductors with hyperscaling violation
我们研究了超标度破坏对全息超导体的影响。在s波模型中，我们发现临界温度随着超标度破坏的增加先减小后增大，并且标量场的质量不会改变超标度破坏的值，从而给出最小的临界温度.我们通过使用具有高阶试函数的Sturm-Liouville方法解析地确认了数值结果，并改进了J. High Energy Phys. { \bf 09}，048（2013）中的先前发现。然而，与s波情况不同的是，我们注意到p波模型的临界温度随着超标度破坏的增加而减小。此外，我们还观察到超标度破坏影响了全息超导体的电导率，并改变了s波和p波模型中带隙频率的预期关系。
We employ the numerical and analytical methods to study the effects of the hyperscaling violation on the ground and excited states of holographic superconductors for $d=2,~z=2$. For both the holographic s-wave and p-wave models with the hyperscaling violation, we observe that the excited state has a lower critical temperature than the corresponding ground state, which is similar to the relativistic case, and the difference of the dimensionless critical chemical potential between the consecutive states decreases as the hyperscaling violation increases. Interestingly, as we amplify the hyperscal…
We study the divergent terms and the finite term in the expansion of the holographic entanglement entropy as the ultraviolet cutoff vanishes for smooth spatial regions having arbitrary shape, when the gravitational background is a four dimensional asymptotically Lifshitz spacetime with hyperscaling violation, in a certain range of the hyperscaling parameter. Both static and time dependent backgrounds are considered. For the coefficients of the divergent terms and for the finite term, analytic expressions valid for any smooth entangling curve are obtained. The analytic results for the finite te…
We investigate the holographic dc conductivity of (2+1) dimensional systems while considering hyperscaling violating geometry in the bulk. We consider Einstein-Maxwell-Dilaton system with two gauge fields and Liouville type potential for dilaton. We also consider axionic fields in the bulk in order to introduce momentum relaxation in the system. We apply an external magnetic field to study the response of the system and obtain analytic expressions for dc conductivity, Hall angle and (thermo)electric conductivity.
We reconsider the holographic model featuring a superconducting dome on the temperature-doping phase diagram with a modified view on the role of the two charges. The first type charge with density $ρ_{A}$ make the Mott insulator, and the second one with $ρ_{B}$ is the extra charge by doping, so that the complex scalar describing the cooper pair condensation couples only with the second charge. We point out that the key role in creating the dome is played by the three point interaction $-c χ^{2} F_{μν}G^{μν}$. The $Tc$ increases with their coupling. We also consider the effect of the quantum cr…
The imaginary potential and entropic force are two important different mechanisms to characterize the dissociation of heavy quarkonia. In this paper, we calculate these two quantities in strongly coupled theories with anisotropic Lifshitz scaling and hyperscaling violation exponent using holographic methods. We study how the results are affected by the hyperscaling violation parameter θ and the dynamical exponent z at finite temperature and chemical potential. Also, we investigate the effect of the chemical potential on these quantities. As a result, we find that both mechanisms show the same …
We analytically compute the thermoelectric conductivities at zero frequency (DC) in the holographic dual of a four dimensional Einstein-Maxwell-Axion-Dilaton theory that admits a class of asymptotically hyperscaling violating Lifshitz backgrounds with a dynamical exponent $z$ and hyperscaling violating parameter $θ$. We show that the heat current in the dual Lifshitz theory involves the energy flux, which is an irrelevant operator for $z>1$. The linearized fluctuations relevant for computing the thermoelectric conductivities turn on a source for this irrelevant operator, leading to several nov…
We study quasinormal modes of shear gravitational perturbations for hyperscaling violating Lifshitz theories, with Lifshitz and hyperscaling violating exponents $z$ and $θ$. The lowest quasinormal mode frequency yields a shear diffusion constant which is in agreement with that obtained in previous work by other methods. In particular for theories with $z< d_i+2-θ$ where $d_i$ is the boundary spatial dimension, the shear diffusion constant exhibits power-law scaling with temperature, while for $z=d_i+2-θ$, it exhibits logarithmic scaling. We then calculate certain 2-point functions of the dual …
In this paper, we holographically quantify the entanglement and complexity for mixed states by following the prescription of purification. The bulk theory we consider in this work is a hyperscaling violating solution, characterized by two parameters, hyperscaling violating exponent $θ$ and dynamical exponent $z$. This geometry is dual to a non-relativistic strongly coupled theory with hidden Fermi surfaces. We first compute the holographic analogy of entanglement of purification (EoP), denoted as the minimal area of the entanglement wedge cross section and observe the effects of $z$ and $θ$. T…
We study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed "complexity = volume" and "complexity = action" dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, in the presence of violations of hyperscaling, there is a parametric enhancement of the action growth rate. We partially match this behavior to simple tensor network models which c…
We study a mathematical relationship between holographic Wilsonian renormalization group and stochastic quantization framework. We extend the original proposal given in arXiv:1209.2242 to interacting theories. The original proposal suggests that fictitious time(or stochastic time) evolution of stochastic 2-point correlation function will be identical to the radial evolution of the double trace operator of certain classes of holographic models, which are free theories in AdS space. We study holographic gravity models with interactions in AdS space and establish a map between the holographic ren…
We develop a formalism with two different UV cutoff scales, one for space and one for time, appropriate for the richer structure of non-Lorentz invariant quantum field theories. In this formalism there are two different beta-functions for each coupling constant, arising from independent variations of the energy or momentum cutoffs. For holographic non-relativistic theories with rotational invariance, we develop the technique to calculate such beta-functions using a generalization of the superpotential formalism developed in [JHEP ${\bf 1208}$, 164 (2012)]. We then proceed and compute the beta-…
On the IR completion of geometries with hyperscaling violation
本文研究了在全息AdS/CFT框架下描述具有动力学临界指数和超标度破坏指数的场论的常磁通量Einstein-Maxwell-Einstein引力问题的解。这样的解决方案是已知的IR-不完全的，由于存在一个运行的量子，这将推动理论在IR中的强耦合，其中量子校正变得重要。在引入一般修正后，本文研究了在视界附近出现AdS_2 x R^2区域的条件，它为超标度违规解提供了IR-完备。在存在这些修正的情况下，我们构造了明确的数值解，其中几何形状从UV中的AdS_4流动到深IR中的AdS_2 x R^2，中间区域既表现出超标度破坏又表现出Lifshitz标度，我们还提供了对Einstein-Maxwell-Maxwell理论结构的限制，以及在红外中出现的AdS_2 x R^2区域。
We consider the magneto-transports of quantum matters doped with magnetic impurities near the quantum critical points(QCP). For this, we first find new black hole solution with hyper-scaling violation which is dual to such system. By considering the fluctuation near this exact solution, we calculated all transport coefficients using the holographic method. We applied our result to the surface state of the topological insulator with magnetic doping and found two QCP's, one bosonic and the other fermionic. It turns out that doped Bi$_2$Se$_3$ and Bi$_2$Te$_3$ correspond to different QCP's. We al…
Using complexity=action proposal we study the growth rate of holographic complexity for Lifshitz and hyperscaling violating geometries. We will consider both one and two sided black branes in an Einstein-Maxwell-Dilaton gravitational theory. We find that in either case Lloyd's bound is violated and the rate of growth of complexity saturates to a value which is greater than twice the mass of the corresponding black brane. This value reduces to the mass of the black brane in the isotropic case. We show that in two sided black brane the saturation happens from above while for one sided black bran…
