It has been realised that corners in entangling surfaces can induce new universal contributions to the entanglement entropy and Rényi entropy. In this paper we study universal corner contributions to entanglement negativity in three- and four-dimensional CFTs using both field theory and holographic techniques. We focus on the quantity χ defined by the ratio of the universal part of the entanglement negativity over that of the entanglement entropy, which may characterise the amount of distillable entanglement. We find that for most of the examples χ takes bigger values for singular entangling regions, which may suggest increase in distillable entanglement. However, there also exist counterexamples where distillable entanglement decreases for singular surfaces. We also explore the behaviour of χ as the coupling varies and observe that for singular entangling surfaces, the amount of distillable entanglement is mostly largest for free theories, while counterexample exists for free Dirac fermion in three dimensions. For holographic CFTs described by higher derivative gravity, χ may increase or decrease, depending on the sign of the relevant parameters. Our results may reveal a more profound connection between geometry and distillable entanglement.

We study corner contributions to holographic entanglement entropy in non-conformal backgrounds: a kink for D2-branes as well as a cone and two different types of crease for D4-branes. Unlike 2 + 1-dimensional CFTs, the corner contribution to the holographic entanglement entropy of D2-branes exhibits a power law behaviour rather than a ogarithmic term. However, the logarithmic term emerges in the holographic entanglement entropy of D4-branes. We identify the logarithmic term for a cone in D4-brane background as the universal contribution under appropriate limits and compare it with other physical quantities.

The N = 2* theory is obtained by deforming N = 4 supersymmetric Yang-Mills theory with two relevant operators of dimensions 2 and 3. We study the holographic entanglement entropy of the N = 2* theory along the whole renormalization group flow. We find that in the UV the holographic entanglement entropy for an arbitrary entangling region receives a universal logarithmic correction, which is related to the relevant operator of dimension 3. This universal behavior can be interpreted on the field theory side by perturbatively evaluating the entanglement entropy of a conformal field theory (CFT) under relevant deformations. In the IR regime, we obtain the large R behavior of the renormalized entanglement entropy for both a strip and a sphere entangling region, where R denotes the size of the entangling region. A term proportional to 1/R is found for both cases, which can be attributed to the emergent CFT5 in the IR.

We study the holographic entanglement entropy of nonlocal field theories at both extremality and finite temperature. The gravity duals, constructed by Nozaki et al. [J. High Energy Phys. 10 (2012) 193], are characterized by a parameter w. Both the zero-temperature backgrounds and the finite-temperature counterparts are exact solutions of Einstein-Maxwell-dilaton theory. For the extremal case we consider the examples where the entangling regions are a strip and a sphere. We find that the leading-order behavior of the entanglement entropy always exhibits a volume law when the size of the entangling region is sufficiently small. We also clarify the condition under which the next-to-leading-order result is universal. For the finite-temperature case we obtain analytic expressions in both the high-temperature and low-temperature limits. In the former case the leading-order result approaches the thermal entropy, while the finite contribution to the entanglement entropy at extremality can be extracted by taking the zero-temperature limit in the latter case. Moreover, we observe some peculiar properties of the holographic entanglement entropy when w = 1.

We study holographic charge transport in (2 + 1) dimensions at finite N, whose dual gravity background is given by perturbative black hole solution in Einstein theory plus cubic terms of Weyl tensor. We consider the higher derivative corrections to the standard Maxwell action, given by the interacting terms between the Weyl tensor and the field strength. We calculate the DC conductivity by using both the membrane paradigm and the Kubo's formula and find precise agreement. We compute the AC conductivity and find an analog of the crossover from "metal" to "bad metal" in the low frequency limit. Moreover, the conductivity becomes a constant in the large frequency limit. We derive two universal relations for the Green's functions and observe that they are exactly the same as the infinite N counterparts.

We consider the holographic entanglement entropy of (d + 2)-dimensional semi-local quantum liquids, for which the dual gravity background in the deep interior is AdS 2 × \( \mathbb{R} \) d multiplied by a warp factor which depends on the radial coordinate. The entropy density of this geometry goes to zero in the extremal limit. The thermodynamics associated with this semi-local background is discussed via dimensional analysis and scaling arguments. For the case of an asymptotically AdS UV completion of this geometry, we show that the entanglement entropy of a strip and an annulus exhibits a phase transition as a typical length of the different shapes is varied, while there is no sign of such a transition for the entanglement entropy of a sphere. Moreover, for the spherical entangling region, the leading order contribution to the entanglement entropy in the IR is calculated analytically. It exhibits an area law behaviour and agrees with the numerical result.

We investigate several aspects of exact black hole solutions in asymptotically Lifshitz spacetime. Firstly,we calculate the tidal forces and find that in the near horizon region of such black hole backgrounds, the tidal forces diverge in the near extremal limit. Secondly, we evaluate the Wilson loops in both extremal and finite temperature cases. Finally, we obtain the corresponding shear viscosity and square of the sound speed and find that the ratio of shear viscosity to entropy density takes the universal value 1/4π in arbitrary dimensions while the square of the speed of sound saturates the conjectured bound 1/3 in five dimensions.

We study striped phases in holographic insulator/superconductor transition by considering a spatially modulated chemical potential in the AdS soliton background. Generally striped phases can develop above a critical chemical potential. When the constant leading term in the chemical potential is set to zero, a discontinuity is observed in the charge density as function of the chemical potential in the limit of large wave vector. We explain this discontinuity using an analytical approach. When the constant leading term in the chemical potential is present, the critical chemical potential is larger than in the case of a homogeneous chemical potential, which indicates that the spatially modulated chemical potential disfavors the phase transition. This behavior is again confirmed by an analytical approach. We also calculate the grand canonical potential and find that the striped phase is favored.

We study dynamics of probe D-branes in (d + 2)-dimensional background with general semilocality. The background is characterized by a parameter eta and is conformal to AdS(2) x R-d. We discuss thermodynamics of the probe D-branes and find that the entropy density is vanishing in the extremal limit, which indicates that the background may correspond to the true ground state of the system. We also clarify the conditions under which the specific heat matches to the behavior of a Fermi liquid or a Bose liquid. We calculate the current-current and density-density retarded Green's functions, from which we can obtain the ac conductivity and the zero sound mode. The ac conductivity scales as omega(-1) when d/eta < 2 and omega(-2 eta/d) when d/eta > 2, while it contains a logarithmic term in omega when d/eta = 2. We also observe that there is no quasiparticle excitation when d/eta >= 2 and classify the conditions under which the quasi-particle description is valid when d/eta < 2.

We study thermodynamics of entanglement entropy for weakly excited states in certain nonconformal field theories, whose gravity duals are given by nonconformal Dp-branes. We observe that the entanglement entropy of a sufficiently small system in nonconformal backgrounds still obeys a first-law-like relation, just as the anti-de Sitter counterparts investigated in [J. Bhattacharya, M. Nozaki, T. Takayanagi, and T. Ugajin, Phys. Rev. Lett. 110, 091602 (2013)]. The effective temperature is proportional to the inverse of the size of the subsystem. The proportionality is a dimensionless constant which is only determined by the shape of the entangling region and independent of any coupling. This universality is confirmed by working with the 10-dimensional string frame metric as well as the lower-dimensional effective metric. When the entangling region is a strip and translational invariance is broken by metric fluctuations, we derive a first-law-like relation where additional components of the stress energy tensor are involved.

We study the DC conductivities of various holographic models using the open string metric (OSM), which is an effective metric geometrizing density and electromagnetic field effect. We propose a new way to compute the nonlinear conductivity using OSM. As far as the final conductivity formula is concerned, it is equivalent to the Karch-O’Bannon’s real-action method. However, it yields a geometrical insight and technical simplifications. Especially, a real-action condition is interpreted as a regular geometry condition of OSM. As applications of the OSM method, we study several holographic models on the quantum Hall effect and strange metal. By comparing a Lifshitz background and the Light-Cone AdS, we show how an extra parameter can change the temperature scaling behavior of conductivity. Finally we discuss how OSM can be used to study other transport coefficients, such as diffusion constant, and effective temperature induced by the effective world volume horizon.

We give a review on our recent work arXiv:1006.0779 [hep-th] and arXiv:1006.1719 [hep-th], in which properties of holographic strange metals were investigated. The background is chosen to be anisotropic scaling solution in Einstein-Maxwell-Dilaton theory with a Liouville potential. The effects of bulk Maxwell field, an extra U (1) gauge field and probe D-branes on the DC conductivity, the DC Hall conductivity and the AC conductivity are extensively analyzed. We classify behaviors of the conductivities according to the parameter ranges in the bulk theory and characterize conditions when the holographic results can reproduce experimental data.

We study charge transport properties in a domain-wall geometry, whose near horizon IR geometry is a Lifshitz black hole and whose UV geometry is AdS. The action for the gauge field contains the standard Maxwell term plus the Weyl tensor coupled to Maxwell field strengths. In four dimensions we calculate the conductivity via both the membrane paradigm and Kubo’s formula. Precise agreements between both methods are obtained. Moreover, we perform an analysis of the four-dimensional electro-magnetic duality in our domain-wall background and find that the relation between the longitudinal and transverse components of the current-current correlation functions and those of the ‘dual’ counterparts holds, irrespective of the near horizon IR geometry. Conductivity at extremality is also investigated. Generalizations to higher dimensions are performed.

We investigate several holographic properties of charged black holes with RF2 corrections, which originate from Kaluza-Klein reductions of five-dimensional Gauss-Bonnet gravity. We obtain the perturbative solution and discuss its thermodynamics. The DC conductivity is calculated via the effective action approach, and the corrections to the DC conductivity are also evaluated. Moreover, we calculate the shear viscosity eta and thermal conductivity kappa(T), as well as two interesting ratios eta/s and kappa(T)mu(2)/(eta T). We find that both bounds conjectured in the literatures can be violated in the presence of the higher- order corrections RF2.

By using the gauge/gravity duality, we investigate the dual field theories of the anisotropic backgrounds, which are exact solutions of Einstein-Maxwell-dilaton theory with a Liouville potential. When we turn on the bulk gauge field fluctuation $A_x$ with a non-trivial dilaton coupling, the AC conductivity of this dual field theory is proportional to the frequency with an exponent depending on parameters of the anisotropic background. In some parameter regions, we find that this conductivity can have the negative exponent like the strange metal. In addition, we also investigate another U(1) gauge field fluctuation, which is not coupled with a dilaton field. We classify all possible conductivities of this system and find that the exponent of the conductivity is always positive.

We investigate zero sound in $D$-dimensional effective holographic theories, whose action is given by Einstein-Maxwell-Dilaton terms. The bulk spacetimes include both zero temperature backgrounds with anisotropic scaling symmetry and their near-extremal counterparts obtained in 1006.2124 [hep-th], while the massless charge carriers are described by probe D-branes. We discuss thermodynamics of the probe D-branes analytically. In particular, we clarify the conditions under which the specific heat is linear in the temperature, which is a characteristic feature of Fermi liquids. We also compute the retarded Green's functions in the limit of low frequency and low momentum and find quasi-particle excitations in certain regime of the parameters. The retarded Green's functions are plotted at specific values of parameters in $D=4$, where the specific heat is linear in the temperature and the quasi-particle excitation exists. We also calculate the AC conductivity in $D$-dimensions as a by-product.

We study several aspects of charged dilaton black holes with planar symmetry in ( d + 2)-dimensional spacetime, generalizing the four-dimensional results investigated in arXiv:0911.3586 [hep-th]. We revisit the exact solutions with both zero and finite temperature and discuss the thermodynamics of the near-extremal black holes. We calculate the AC conductivity in the zero-temperature background by solving the corresponding Schrödinger equation and find that the AC conductivity behaves like ω δ , where the exponent δ is determined by the dilaton coupling α and the spacetime dimension parameter d . Moreover, we also study the Gauss-Bonnet corrections to η / s in a five-dimensional finite-temperature background.

We continue our analysis on conductivity in the anisotropic background by employing the D-brane probe technique, where the D-branes play the role of charge carriers. The DC and AC conductivity for massless charge carriers are obtained analytically, while interesting curves for the AC conductivity are also plotted. For massive charge carriers, we calculate the DC and AC conductivities in the dilute limit and we fix the parameters in the Einstein-Maxwell-dilaton theory so that the background exhibits the same scaling behaviors as those for real-world strange metals. The DC conductivity at finite density is also computed.

We investigate properties of holographic strange metals in p + 2 dimensions, generalizing the analysis performed in [S. A. Hartnoll et al. J. High Energy Phys. 04 (2010) 120]. The bulk spacetime is a p + 2-dimensional Lifshitz black hole, while the role of charge carriers is played by probe D-branes. We mainly focus on massless charge carriers, where most of the results can be obtained analytically. We obtain exact results for the free energy and calculate the entropy density and the heat capacity, as well as the speed of sound at low temperature. We obtain the DC conductivity and DC Hall conductivity and find that the DC conductivity takes a universal form in the large density limit, while the Hall conductivity is also universal in all dimensions. We also study the resistivity in different limits and clarify the condition for the linear dependence on the temperature, which is a key feature of strange metals. We show that our results for the DC conductivity are consistent with those obtained via the Kubo formula and we obtain the charge diffusion constant analytically. The corresponding properties of massive charge carriers are also discussed in brief.