Takuya Tsukioka

Viscosity bound, causality violation and instability with stringy correction and charge

Recently, it has been shown that if we consider the higher derivative correction, the viscosity bound conjectured to be ?/s = 1/4? is violated and so is the causality. In this paper, we consider medium effect and the higher derivative correction simultaneously by adding charge and Gauss-Bonnet terms. We find that the viscosity bound violation is not changed by the charge. However, we find that two effects together create another instability for large momentum regime. We argue the presence of tachyonic modes and show it numerically. We draw a phase diagram relevant to the instability in charge-coupling space.

Another realization of Kerr/CFT correspondence

Abstract We study another realization of the Kerr/CFT correspondence. By imposing new asymptotic conditions for the near-horizon geometry of Kerr black hole, an asymptotic symmetry which contains all of the exact isometries can be obtained. In particular, the Virasoro algebra can be realized as an enhancement of SL ( 2 , R ) symmetry of the AdS geometry. By using this asymptotic symmetry, we discuss finite temperature effects and show the correspondence concretely.

Holographic QCD: Past, Present, and Future

At the dawn of a new theoretical tool based on the AdS/CFT correspondence for non-perturbative aspects of quantum chromodynamics, we give an interim review on the new tool, holographic QCD, with some of its accomplishment. We try to give an A-to-Z picture of the holographic QCD, from string theory to a few selected top-down holographic QCD models with one or two physical applications in each model. We may not attempt to collect diverse results from various holographic QCD model studies.

Density Dependence of Transport Coefficients from Holographic Hydrodynamics

We study the transport coefficients of Quark-Gluon-Plasma in finite temperature and finite baryon density. We consider AdS/QCD of charged AdS black hole background with bulk-filling branes identifying the U (1) charge as the baryon number. Using Reissner

Yet another realization of Kerr/CFT correspondence

The correspondence between the Kerr black hole and a boundary CFT has been conjectured recently. The conjecture has been proposed first only for the half of the CFT, namely for left movers. For right movers, the correspondence has been also found out through the suitable asymptotic boundary condition. However, the boundary conditions for these two studies are exclusive to each other. The boundary condition for left movers does not allow the symmetry of right movers, and vice versa. We propose a new boundary condition which allows both left and right movers. The isometries U(1) for the left mover and the for right mover are enhanced to Virasoro algebras with and without central extensions, respectively.

Chern-Simons term in holographic hydrodynamics of charged AdS black hole

We study the effects of the Chern-Simons term in the hydrodynamics of the five-dimensional Reissner-Nordstr¨om-AdS background. We work out the decoupling problem of the equations of motion and calculate the retarded Green functions explicitly. We then find that the Chern-Simons term induces the magnetic conductivity caused by the anomaly effect. It is increasing function of temperature running from a non-zero value at zero temperature to the twice the value at infinite temperature.

Conformal symmetry for rotating D-branes

Abstract We apply the Kerr/CFT correspondence to the rotating black p-brane solutions. These solutions give the simplest examples from string theory point of view. Their near horizon geometries have structures of AdS, even though black p-brane solutions do not have AdS-like structures in the non-rotating case. The microscopic entropy which can be calculated via the Cardy formula exactly agrees with Bekenstein–Hawking entropy.

Sound Modes in Holographic Hydrodynamics for Charged AdS Black Hole

Abstract In the previous paper we studied the transport coefficients of quark–gluon plasma in finite temperature and finite density in vector and tensor modes. In this paper, we extend it to the scalar modes. We work out the decoupling problem and hydrodynamic analysis for the sound mode in charged AdS black hole and calculate the sound velocity, the charge susceptibility and the electrical conductivity. We find that Einstein relation among the conductivity, the diffusion constant and the susceptibility holds exactly.

Notes on the hidden conformal symmetry in the near horizon geometry of the Kerr black hole

Abstract Toward the Kerr/CFT correspondence for the generic non-extremal Kerr black hole, the analysis of scattering amplitudes by near extremal Kerr provides a clue. This pursuit reveals a hidden conformal symmetry in the low frequency wave equation for a scalar field in a certain spacetime region referred to as the near region. For extremal case, the near region is expected to be the near horizon region in which the correspondence via the asymptotic symmetry is studied. We investigate the hidden conformal symmetry in the near horizon limit and consider the relation between the hidden conformal symmetry and the asymptotic symmetry in the near horizon limit. By using an appropriate definition of the quasi-local charge, we obtain the deviation of the entropy from the extremality.We present here an approach to a computation of ζ(2) by changing variables in the double integral using hyperbolic trig functions. We also apply this approach to present ζ(n), when n > 2, as a definite improper integral of single variable.

Quark number susceptibility with finite chemical potential in holographic QCD

We study the quark number susceptibility in holographic QCD with a finite chemical potential or under an external magnetic field at finite temperature. We first consider the quark number susceptibility with the chemical potential. We observe that approaching Tc from high temperature regime, χq/T2 develops a peak as we increase the chemical potential, which confirms recent lattice QCD results. We discuss this behavior in connection with the existence of the critical end point in the QCD phase diagram. We also consider the quark number susceptibility under the external magnetic field. We predict that the quark number susceptibility exhibits a blow-up behavior at low temperature as we raise the value of the magnetic field. We finally spell out some limitations of our study.