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We have considered non-conformal fluid dynamics whose gravity dual is a certain Einstein dilaton system with Liouville type dilaton potential, characterized by an intrinsic parameter $eta$. We have discussed the Hawking-Page transition in this framework using hard-wall model and it turns out that the critical temperature of the Hawking-Page transition encapsulates a non-trivial dependence on $eta$. We also obtained transport coefficients such as AC conductivity, shear viscosity and diffusion constant in the hydrodynamic limit, which show non-trivial $eta$ dependent deviations from those in conformal fluids, although the ratio of the shear viscosity to entropy density is found to saturate the universal bound. Some of the retarded correlators are also computed in the high frequency limit for case study.
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In the AdS$_3$/CFT$_2$ correspondence, we find some conformal field theory (CFT) states that have no bulk description by the Ba~nados geometry. We elaborate the constraints for a CFT state to be geometric, i.e., having a dual Ba~nados metric, by comparing the order of central charge of the entanglement/Renyi entropy obtained respectively from the holographic method and the replica trick in CFT. We find that the geometric CFT states fulfill Bohrs correspondence principle by reducing the quantum KdV hierarchy to its classical counterpart. We call the CFT states that satisfy the geometric constraints geometric states, and otherwise non-geometric states. We give examples of both the geometric and non-geometric states, with the latter case including the superposition states and descendant states.
Holographic mutual and tripartite information have been studied in a non-conformal background. We have investigated how these observables behave as the energy scale and number of degrees of freedom vary. We have found out that the effect of degrees of freedom and energy scale is opposite. Moreover, it has been observed that the disentangling transition occurs at large distance between sub-systems in non-conformal field theory independent of l. The mutual information in a non-conformal background remains also monogamous.
In this work we will study the low-energy collective behavior of spatially anisotropic dense fluids in four spacetime dimensions. We will embed a massless flavor D7-brane probe in a generic geometry which has a metric possessing anisotropy in the spatial components. We work out generic formulas of the low-energy excitation spectra and two-point functions for charged excitations at finite baryon chemical potential. In addition, we specialize to a certain Lifshitz geometry and discuss in great detail the scaling behavior of several different quantities.
Gravity/fluid correspondence becomes an important tool to investigate the strongly correlated fluids. We carefully investigate the holographic fluids at the finite cutoff surface by considering different boundary conditions in the scenario of gravity/fluid correspondence. We find that the sonic velocity of the boundary fluids at the finite cutoff surface is critical to clarify the superficial similarity between bulk viscosity and perturbation of the pressure for the holographic fluid, where we set a special boundary condition at the finite cutoff surface to explicitly express this superficial similarity. Moreover, we further take the sonic velocity into account to investigate a case with more general boundary condition. In this more general case, two parameters in the first order stress tensor of holographic fluid cannot be fixed, one can still extract the information of transport coefficients by considering the sonic velocity seriously.
The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex fixed points are close to the real axis, the system typically exhibits walking behavior with Miransky (or Berezinsky-Kosterlitz-Thouless) scaling. We present a novel realization of these phenomena at strong coupling by means of the gauge/gravity duality, and give evidence for the conjectured existence of complex conformal field theories at the fixed points.
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