Hyperscaling Violation Exponent Research Articles

Gravitational Waves of Holographic QCD Phase Transition with Hyperscaling Violation

In this paper, we study the gravitational waves of holographic QCD phase transition with hyperscaling violation. We consider an Einstein–Maxwell Dilaton background and discuss the confinement–deconfinement phase transition between thermally charged AdS and AdS black holes. We find that hyperscaling violation reduces the phase transition temperature. In a further study, we discuss the effect of hyperscaling violation on the GW spectrum. We found that the hyperscaling violation exponent suppresses the peak frequency of the total GW spectrum. Moreover, the results of the GW spectrum may be detected by IPTA, SKA, BBO, and NANOGrav. We also find that the hyperscaling violation exponent suppresses the peak frequency of the bubble-collision spectrum h2Ωenv. Hyperscaling violation enhances the energy densities of the sound wave spectrum h2Ωsw and the MHD turbulence spectrum h2Ωturb. The total GW spectrum is dominated by the contribution of the bubble collision in runaway bubbles case.

Holographic study of Toverline{T} like deformed HV QFTs: holographic entanglement entropy

We study the (d + 2)-dimensional Hyperscaling Violating (HV) geometries in the presence of both a finite temperature T and a UV cutoff rc. This gravitational system is conjectured to be dual to Toverline{T} like deformed HV QFTs. We consider the representative quantum entanglement quantity in holography, i.e. the entanglement entropy S(A), and perform a complete analysis in all possible parameter ranges of the hyperscaling violation exponent θ and the critical dynamical exponent z to study the effect of the temperature and the cutoff. We find that the temperature has a universal effect independent of the parameters: it enhances S(A) in the small cutoff limit, while it is irrelevant in the large cutoff limit. For the cutoff effect, we find that the cutoff monotonically suppresses S(A) where its behavior depends on the parameter range. As an application of the finite temperature analysis, we study the first law of entanglement entropy, ST – ST =0 ~ ℓλ, in the small subsystem size ℓ limit. We find that λ interpolates between λ = 1 + z in the small cutoff and λ = 3 in the large cutoff, independent of the parameter range. We also provide the analytic holographic result at z = d – θ and discuss its possibility of comparison with the field theoretic result.

Generalized volume-complexity for two-sided hyperscaling violating black branes

In this paper, we investigate generalized volume-complexity mathcal{C} gen for a two-sided uncharged HV black brane in d + 2 dimensions. This quantity which was recently introduced in [48], is an extension of volume in the Complexity=Volume (CV) proposal, by adding higher curvature corrections with a coupling constant λ to the volume functional. We numerically calculate the growth rate of mathcal{C} gen for different values of the hyperscaling violation exponent θ and dynamical exponent z. It is observed that mathcal{C} gen always grows linearly at late times provided that we choose λ properly. Moreover, it approaches its late time value from below. For the case λ = 0, we find an analytic expression for the late time growth rate for arbitrary values of θ and z. However, for λ ≠ 0, the late time growth rate can only be calculated analytically for some specific values of θ and z. We also examine the dependence of the growth rate on d, θ, z and λ. Furthermore, we calculate the complexity of formation obtained from volume-complexity and show that it is not UV divergent. We also examine its dependence on the thermal entropy and temperature of the black brane. At the end, we also numerically calculate the growth rate of mathcal{C} gen for the case where the higher curvature corrections are a linear combination of the Ricci scalar, square of the Ricci tensor and square of the Riemann tensor. We show that for appropriate values of the coupling constants, the late time growth rate is again linear.

Entropy of Hawking radiation for two-sided hyperscaling violating black branes

In this paper, we study the von Neumann entropy of Hawking radiation SR for a d + 2-dimensional Hyperscaling Violating (HV) black brane which is coupled to two Minkowski spacetimes as the thermal baths. We consider two different situations for the matter fields: first, they are described by a CFTd+2 whose central charge c is very large. Second, they are described by a d+2 dimensional HV QFT which has a holographic gravitational theory that is a HV geometry at zero temperature. For both cases, we calculate the Page curve of the Hawking radiation as well as the Page time tPage. For the first case, SR grows linearly with time before the Page time and saturates after this time. Moreover, tPage is proportional to frac{2{S}_{mathrm{th}}}{cT} , where Sth and T are the thermal entropy and temperature of the black brane. For the second case, when the hyperscaling violation exponent θm of the matter fields is zero, the results are very similar to those for the first case. However, when θm ≠ 0, the entropy of Hawking radiation grows exponentially before tPage and saturates after this time. Furthermore, the Page time is proportional to log left(frac{1}{G_{mathrm{N},mathrm{r}}}right) , where GN,r is the renormalized Newton’s constant. It was also observed that for both cases, tPage is a decreasing and an increasing function of the dynamical exponent z and hyperscaling violation exponent θ of the black brane geometry, respectively. Moreover, for the second case, tPage is independent of zm, and for θm ≠ 0, it is a decreasing function of θm.

Entropic destruction of heavy quarkonium with hyperscaling violation * *Supported by the Innovation Fund of Key Laboratory of Quark and Lepton Physics (QLPL2020P01)

We study the entropic destruction of heavy quarkonium in strongly coupled theories with an anisotropic scaling symmetry in time and a spatial direction. We consider Lifshitz and hyperscaling violation theories, which are covariant under a generalized Lifshitz scaling symmetry with the dynamical exponent z and hyperscaling violation exponent . It is shown that the entropic force depends on the parameters of these theories. In particular, increasing z decreases the entropic force, thus reducing the quarkonium dissociation, while increasing has the opposite effect.

Effects of the hyperscaling violation and dynamical exponents on the imaginary potential and entropic force of heavy quarkonium via holography

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 theta 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 results: the thermal width and the dissociation length decrease as the dynamical exponent and chemical potential increase or as the hyperscaling violating parameter decreases.

On Casimir Energy and Mutual Information in Non-relativistic Backgrounds

We apply the AdS/CFT correspondence in considering the Casimir energy and some non-local entanglement measures in the non-relativistic backgrounds for general dynamical exponent z with and without hyperscaling violation exponent 𝜃. In such background, we use holographic methods and compute the mutual information and tripartite information. We also consider the monogamy of holographic mutual information in the Schrodinger-type geometry and by numerical analysis we show that this quantity is monogamous.

Chaotic dynamics of string around charged black brane with hyperscaling violation

By fast Lyapunov indicator (FLI), we study the chaotic dynamics of closed string around charged black brane with hyperscaling violation (HV). The Hawking temperature, Lifshitz dynamical exponent and HV exponent together affect the chaotic dynamics of this system. The temperature plays the role of driving the closed string to escape to infinity. There is a threshold value z∗ = 2, below which the string is captured by the black brane no matter where the string is placed at the beginning. However, when z > 2, the string escapes to infinity if it is placed near the black brane at the beginning, but if the initial position of string is far away from the black brane, it oscillates around the black brane till eternity, which is a quasi-periodic motion. HV exponent plays the role of driving the string falling into the black brane. With the increase of HV exponent θ, the falling velocity becomes faster. We find that when we heat the system with large HV exponent, the chaotic system does not essentially changes. It indicates that the HV exponent plays a very important role in determining the state of the chaotic system. Also we study the effect from the winding number of the string. The study indicates that the chaotic dynamics of the string is insensitive to the winding number.

Effects of hyperscaling violation and dynamical exponents on heavy quark potential and jet quenching parameter

In this paper, we investigate the heavy quark potential and the jet quenching parameter in a system with Lifshitz and hyperscaling violation exponents, by using the AdS/CFT correspondence. It is shown that the heavy quark potential and the jet quenching parameter are dependent upon the nonrelativistic parameters. We show how the heavy quark potential changes with the hyperscaling violation parameter theta , dynamical parameter z, temperature T and charge Q. Increasing z and theta lead to increasing and decreasing the potential respectively. The potential decreases and increases by increasing Q and T. It is investigated how the jet quenching parameter changes with the hyperscaling violation parameter theta and dynamical parameter z. Also, we add some electromagnetic field and obtain its effect on the jet quenching parameter and see as z and theta increasing this parameter decreases and the electric and magnetic fields affect differently on that.

Strongly Coupled Anisotropic Gauge Theories and Holography.

We initiate a nonperturbative study of anisotropic, nonconformal, and confining gauge theories that are holographically realized in gravity by generic Einstein-axion-dilaton systems. In the vacuum, our solutions describe renormalization group flows from a conformal field theory in the UV to generic scaling solutions in the IR with generic hyperscaling violation and dynamical exponents θ and z. We formulate a generalization of the holographic c theorem to the anisotropic case. At finite temperature, we discover that the anisotropic deformation reduces the confinement-deconfinement phase transition temperature suggesting a possible alternative explanation of inverse magnetic catalysis solely based on anisotropy. We also study transport and diffusion properties in anisotropic theories and observe, in particular, that the butterfly velocity that characterizes both diffusion and growth of chaos transverse to the anisotropic direction saturates a constant value in the IR which can exceed the bound given by the conformal value.

Effects of hyperscaling violation and dynamical exponents on drag force

In this paper, we calculate the drag force of a charged particle in systems with hyperscaling violation using the AdS/CFT correspondence. We obtain energy loss, friction coefficient, diffusion and quasi normal modes of a heavy point particle. Here, we consider two cases. In the first, we assume the heavy point particle moves with constant velocity v. In the second case, we assume the heavy point particle rotates along a circle of radius L with angular velocity ω. Also, we add some electromagnetic field and obtain the energy loss. Finally, we draw some figures for the drag force with respect to the velocity and the temperature. As well, we show how the drag force and energy loss change with the hyperscaling violation parameter θ, dynamical parameter z, mass m and charge Q.

Hyperscaling violating black hole solutions and magneto-thermoelectric DC conductivities in holography

We derive new black hole solutions in Einstein-Maxwell-Axion-Dilaton theory with a hyperscaling violation exponent. We then examine the corresponding anomalous transport exhibited by cuprate strange metals in the normal phase of high-temperature superconductors via gauge/gravity duality. Linear temperature dependence resistivity and quadratic temperature dependence inverse Hall angle can be achieved. In the high temperature regime, the heat conductivity and Hall Lorenz ratio are proportional to the temperature. The Nernst signal first increases as temperature goes up but it then decreases with increasing temperature in the high temperature regime.

Non-relativistic anyons from holography

We study generic types of holographic matter residing in Lifshitz invariant defect field theory as modeled by adding probe D-branes in the bulk black hole spacetime characterized by dynamical exponent z and with hyperscaling violation exponent θ. Our main focus will be on the collective excitations of the dense matter in the presence of an external magnetic field. Constraining the defect field theory to 2+1 dimensions, we will also allow the gauge fields become dynamical and study the properties of a strongly coupled anyonic fluid. We will deduce the universal properties of holographic matter and show that the Einstein relation always holds.

Heavy Quark Potential with Hyperscaling Violation

We investigate the behavior of the heavy quark potential in the backgrounds with hyperscaling violation. The metrics are covariant under a generalized Lifshitz scaling symmetry with the dynamical Lifshitz parameter z and hyperscaling violation exponent θ. We calculate the potential for a certain range of z and θ and discuss how it changes in the presence of the two parameters. Moreover, we add a constant electric field to the backgrounds and study its effects on the potential. It is shown that the heavy quark potential depends on the nonrelativistic parameters. Also, the presence of the constant electric field tends to increase the potential.

Black hole microstates in anti–de Sitter space

We extend a recently derived higher-dimensional Cardy formula to include angular momenta, which we use to obtain the Bekensten-Hawking entropy of anti-de Sitter black branes, compactified rotating branes, and large Schwarzschild/Kerr black holes. This is the natural generalization of Strominger's microscopic derivation of the Banados-Teitelboim-Zanelli black hole entropy to higher dimensions. We propose an extension to include $U(1)$ charge, which agrees with the Bekenstein-Hawking entropy of large Reissner-Nordstrom/Kerr-Newman black holes at high temperature. We extend the results to an arbitrary hyperscaling-violation exponent (this captures the case of black $Dp$-branes as a subclass) and reproduce logarithmic corrections.

Area law for gapless states from local entanglement thermodynamics

We demonstrate an area law bound on the ground state entanglement entropy of a wide class of gapless quantum states of matter using a strategy called local entanglement thermodynamics. The bound depends only on thermodynamic data, actually a single exponent, the hyper-scaling violation exponent $\theta$. All systems in $d$ spatial dimensions obeying our scaling assumptions and with $\theta < d-1$ obey the area law, while systems with $\theta = d-1$ can violate the area law at most logarithmically. We also discuss the case of frustration-free Hamiltonians and show that to violate the area law more than logarithmically these systems must have an unusually large number of low energy states. Finally, we make contact with the recently proposed $s$-source framework and argue that $\theta$ and $s$ are related by $s=2^\theta$.

Entanglement temperature for black branes with hyperscaling violation

Entanglement temperature is an interesting quantity which relates the increased amount of entanglement entropy to that of energy for a weakly excited state in the first-law of entanglement entropy, it is proportional to the inverse of the size of entanglement subsystem and only depends on the shape of the entanglement region. We find the explicit formula of entanglement temperature for the general hyperscaling violation backgrounds with a strip-subsystem. We then investigate the entanglement temperature for a round ball-subsystem, we check that the entanglement temperature has a universal form when the hyperscaling violation exponent is near zero.

Scalar boundary conditions in hyperscaling violating geometry

We study the possible boundary conditions of scalar field modes in a hyperscaling violation (HV) geometry with Lifshitz dynamical exponent z(z≥1) and hyperscaling violation exponent θ (θ≠0). For the case with θ>0, we show that in the parameter range 1≤z≤2, −z+d−1<θ≤(d−1)(z−1) or z>2, −z+d−1<θ≤d−1, the boundary conditions have different types, including the Neumann, Dirichlet and Robin conditions, while in the range θ≤−z+d−1, only Dirichlet type condition can be set. In particular, we further confirm that the mass of the scalar field does not play any role in determining the possible boundary conditions for θ>0, which has been addressed in Ref. [1]. Meanwhile, we also carry out the parallel investigation in the case with θ<0. We find that for m2<0, three types of boundary conditions are available, but for m2>0, only one type is available.

Dynamically generated gap from holography in the charged black brane with hyperscaling violation

We holographically investigate the effects of a dipole coupling between a fermion field and a $U(1)$ gauge field on the dual fermionic sector in the charged gravity bulk with hyperscaling violation. We analytically study the features of the ultraviolet and infrared Green's functions of the dual fermionic system and we show that as the dipole coupling and the hyperscaling violation exponent are varied, the fluid possess Fermi, marginal Fermi, non-Fermi liquid phases and also an additional Mott insulating phase. We find that the increase of the hyperscaling violation exponent which effectively reduces the dimensionality of the system makes it harder for the Mott gap to be formed. We also show that the observed duality between zeros and poles in the presence of a dipole moment coupling still persists in theories with hyperscaling violation.

Interpolating solution fromAdS5to hyperscaling violating Lifshitz spacetime

We construct two interpolating solutions in type II string theory which interpolate between an AdS$_5$ in the UV and a hyperscaling violating three (spatial) dimensional Lifshitz space-time in the IR. The first solution is non-supersymmetric and is obtained from a known intersecting non-supersymmetric D3-brane with chargeless D0-brane solution of type IIB string theory, by restricting some parameters characterizing the solution and going to a new coordinate. In the IR the dilaton is non-constant in general and the metric is three (spatial) dimensional hyperscaling violating Lifshitz with dynamical critical exponent $z=(3+3\gamma)/(3-\gamma)$ and hyperscaling violation exponent $\theta = 12/(3-\gamma)$, where $\gamma$ is a real parameter and can take continuous values from $-1$ to $+1$. At the two extreme values, i.e., for $\gamma = \pm 1$, the dilaton is constant. The second solution is supersymmetric and is obtained from the known F-D2 bound state solution of type IIA string theory by zooming into a particular region of space. In the UV, the proper description is given in a T-dual frame which is AdS$_5$, whereas in the IR, it gives a three dimensional hyperscaling violating Lifshitz with $z=3$ and $\theta=2=d-1$.