Makoto Natsuume

Viscosity of gauge theory plasma with a chemical potential from AdS/CFT correspondence

We compute the strong coupling limit of the shear viscosity for the N=4 super-Yang-Mill theory with a chemical potential. We use the five-dimensional Reissner-Nordstroem-anti-deSitter black hole, so the chemical potential is the one for the R-charges U(1){sub R}{sup 3}. We compute the quasinormal frequencies of the gravitational and electromagnetic vector perturbations in the background numerically. This enables one to explicitly locate the diffusion pole for the shear viscosity. The ratio of the shear viscosity {eta} to the entropy density s is {eta}/s=1/(4{pi}) within numerical errors, which is the same result as the one without chemical potential.

Vortex lattice for a holographic superconductor

We investigate the vortex lattice solution in a (2+1)-dimensional holographic model of superconductors constructed from a charged scalar condensate. The solution is obtained perturbatively near the second-order phase transition and is a holographic realization of the Abrikosov lattice. Below a critical value of the magnetic field, the solution has a lower free energy than the normal state. Both the free-energy density and the superconducting current are expressed by nonlocal functions, but they reduce to the expressions in the Ginzburg-Landau theory at long wavelengths. As a result, a triangular lattice becomes the most favorable solution thermodynamically, as in the Ginzburg-Landau theory of type II superconductors.

Screening length in plasma winds

We study the screening length Ls of a heavy quark-antiquark pair in strongly coupled gauge theory plasmas flowing at velocity v. Using the AdS/CFT correspondence we investigate, analytically, the screening length in the ultra-relativistic limit. We develop a procedure that allows us to find the scaling exponent for a large class of backgrounds. We find that for conformal theories the screening length is (boosted energy density)−1/d. As examples of conformal backgrounds we study R-charged black holes and Schwarzschild-anti-deSitter black holes in (d+1)-dimensions. For non-conformal theories, we find that the exponent deviates from −1/d. As examples we study the non-extremal Klebanov-Tseytlin and Dp-brane geometries. We find an interesting relation between the deviation of the scaling exponent from the conformal value and the speed of sound.

Dynamic critical phenomena in the AdS/CFT duality

In critical phenomena, singular behaviors arise not only for thermodynamic quantities but also for transport coefficients. We study this dynamic critical phenomenon in the AdS/CFT duality. We consider black holes with a single R-charge in various dimensions and compute the R-charge diffusion in the linear perturbations. In this case, the black holes belong to model B according to the classification of Hohenberg and Halperin.

The Shear Viscosity of Holographic Superfluids

We study the ratio of the shear viscosity to the entropy density for various holographic superfluids. For the s-wave case, the ratio has the universal value 1/(4π )a s in various holographic models. For the p-wave case, there are two shear viscosity coefficients because of the anisotropic boundary spacetime, and one coefficient has the universal value. For the (p + ip)-wave case, the existing technique is not applicable since there is no tensor mode of metric perturbations which decouples from Yang-Mills perturbations. Our results indicate that the shear viscosity does not show a singular behavior at the critical point for holographic superfluids. Subject Index: 121

A Note on causal hydrodynamics for M-theory branes

The AdS/CFT duality is a powerful tool to study hydrodynamics of gauge theory plasmas (see Ref. 1) for a review). However, standard hydrodynamics (first-order formalism) has severe problems such as acausality. One can restore causality by introducing a new set of transport coefficients. The resulting theory is known as “causal hydrodynamics” or “second-order formalism”. At present, there is no unique formalism for causal hydrodynamics, but probably the most used formalism is the “Israel-Stewart theory”.2),3) The Israel-Stewart theory has been widely discussed in the context of heavy-ion collisions. Recently, a number of papers appeared which study the causal hydrodynamics of gauge theory plasmas using the AdS/CFT duality.4)−8),∗∗∗) Some of the main lessons drawn from these works are, 1. One should not take the Israel-Stewart theory too literally; it should be really considered as an effective theory. For example, a single transport coefficient τπ appears both in the “shear mode” and in the “sound mode”. However, if one naively uses the Israel-Stewart theory to interpret the AdS/CFT results, two different values arise. Reference 5) argues that the shear mode result is unreliable due to the corrections from “third-order” hydrodynamics. Namely, the shear mode case exceeds the validity of the effective theory. References 5) and 7) confirmed this for SAdS5,†) and Ref. 7) confirmed this for SAdS4 and SAdS7 as well. 2. Reference 5) proposed a Kubo-like formula for conformal theories to obtain τπ from the “tensor mode”. The formula yields the value of τπ which appears in the sound mode for SAdS5.We suggest an explanation for the twin kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binaries (LMXBs) based on magnetohydrodynamics (MHD) oscillation modes in neutron star magnetospheres. Including the effect of the neutron star spin, we derive several MHD wave modes by solving the dispersion equations, and propose that the coupling of the two resonant MHD modes may lead to the twin kHz QPOs. This model naturally relates the upper, lower kHz QPO frequencies with the spin frequencies of the neutron stars, and can well account for the measured data of six LMXBs.

Quasinormal modes for nonextreme Dp-branes and thermalizations of super-Yang-Mills theories

The nonextreme Dp-brane solutions in type II supergravity (in the near-horizon limit) are expected to be dual to (p+1)-dimensional noncompact supersymmetric Yang-Mills theories at finite temperature. We study the translationally invariant perturbations along the branes in those backgrounds and calculate quasinormal frequencies numerically. These frequencies should determine the thermalization time scales in the dual Yang-Mills theories.

String theory implications on causal hydrodynamics

We summarize the main lessons for causal hydrodynamics/second order hydrodynamics/Israel-Stewart theory from string theory.

Two pieces of folklore in the AdS/CFT duality

In the AdS/CFT duality, it is often said that a local symmetry in a bulk theory corresponds to a global symmetry in the corresponding boundary theory, but the global symmetry can become local when one couples with an external source. As a result, the Gubser-Klebanov-Polyakov-Witten relation gives a response function instead of a Green function. We explore this point in detail using the example of holographic superconductors. We point out that these points play a crucial role in interpreting the holographic London equation properly.

Screening length and the direction of plasma winds

We study the screening length of a heavy quark-antiquark pair in strongly coupled gauge theory plasmas flowing at velocity v following a proposal by Liu, Rajagopal, and Wiedemann. We analyze the screening length as the direction of the plasma winds vary. To leading order in v, this angle-dependence can be studied analytically for many theories by extending our previous formalism. We show that the screening length is locally a minimum (maximum) when the pair is perpendicular (parallel) to the plasma winds, which has been observed for the = 4 plasma. Also, we compare AdS/CFT results with weak coupling ones, and we discuss the subleading dependence on v for the Dp-brane.