Norihiro Iizuka

Holography of dyonic dilaton black branes

We study black branes carrying both electric and magnetic charges in Einstein-Maxwell theory coupled to a dilaton-axion in asymptotically anti de Sitter space. After reviewing and extending earlier results for the case of electrically charged branes, we characterise the thermodynamics of magnetically charged branes. We then focus on dyonic branes in theories which enjoy an SL(2,R) electric-magnetic duality. Using SL(2,R), we are able to generate solutions with arbitrary charges starting with the electrically charged solution, and also calculate transport coefficients. These solutions all exhibit a Lifshitz-like near-horizon geometry. The system behaves as expected for a charged fluid in a magnetic field, with non-vanishing Hall conductance and vanishing DC longitudinal conductivity at low temperatures. Its response is characterised by a cyclotron resonance at a frequency proportional to the magnetic field, for small magnetic fields. Interestingly, the DC Hall conductance is related to the attractor value of the axion. We also study the attractor flows of the dilaton-axion, both in cases with and without an additional modular-invariant scalar potential. The flows exhibit intricate behaviour related to the duality symmetry. Finally, we briefly discuss attractor flows in more general dilaton-axion theories which do not enjoy SL(2,R) symmetry.

Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity

A bstractWe study the two-point function for fermionic operators in a class of strongly coupled systems using the gauge-gravity correspondence. The gravity description includes a gauge field and a dilaton which determines the gauge coupling and the potential energy. Extremal black brane solutions in this system typically have vanishing entropy. By analyzing a charged fermion in these extremal black brane backgrounds we calculate the two-point function of the corresponding boundary fermionic operator. We find that in some region of parameter space it is of Fermi liquid type. Outside this region no well-defined quasi-particles exist, with the excitations acquiring a non-vanishing width at zero frequency. At the transition, the two-point function can exhibit non-Fermi liquid behaviour.

Bianchi attractors: a classification of extremal black brane geometries

A bstractExtremal black branes are of interest because they correspond to the ground states of field theories at finite charge density in gauge/gravity duality. The geometry of such a brane need not be translationally invariant in the spatial directions along which it extends. A less restrictive requirement is that of homogeneity, which still allows points along the spatial directions to be related to each other by symmetries. In this paper, we find large new classes of homogeneous but anisotropic extremal black brane horizons, which could naturally arise in gauge/gravity dual pairs. In 4+1 dimensional spacetime, we show that such homogeneous black brane solutions are classified by the Bianchi classification, which is well known in the study of cosmology, and fall into nine classes. In a system of Einstein gravity with negative cosmological term coupled to one or two massive Abelian gauge fields, we find solutions with an additional scaling symmetry, which could correspond to the near-horizon geometries of such extremal black branes. These solutions realize many of the Bianchi classes. In one case, we construct the complete extremal solution which asymptotes to AdS space.

Study of anisotropic black branes in asymptotically anti-de Sitter

A bstractWe investigate the four dimensional gravitational theories which admit homogeneous but anisotropic black brane solutions in asymptotically AdS space-time. The gravitational theories we consider are 1) Einstein-Maxwell-dilaton theory, and 2) EinsteinMaxwell-dilaton-axion theory with SL(2, R) symmetry. We obtain the solutions both analytically and numerically. Analytical solutions are obtained by perturbation from the isotropic solutions. Our solutions approach singular behavior at the horizon in the extremal limit but in non-extremal case, they are smooth everywhere. We also discuss how the third law of thermodynamics holds in our set-up.

Rapid Thermalization by Baryon Injection in Gauge/Gravity Duality

Using the AdS/CFT correspondence for strongly coupled gauge theories, we calculate thermalization of mesons caused by a time-dependent change of a baryon number chemical potential. On the gravity side, the thermalization corresponds to a horizon formation on the probe flavor brane in the AdS throat. Since heavy ion collisions are locally approximated by a sudden change of the baryon number chemical potential, we discuss implication of our results to RHIC and LHC experiments, to find a rough estimate of rather rapid thermalization time-scale t_{th} < 1 [fm/c]. We also discuss universality of our analysis against varying gauge theories.

A matrix model for baryons and nuclear forces

We propose a new matrix model describing multi-baryon systems. We derive the action from open string theory on the wrapped baryon vertex D-branes embedded in the D4-D8 model of large Nc holographic QCD. The positions of k baryons are unified into k × k matrices, with spin/isospin of the baryons encoded in a set of k-vectors. Holographic baryons are known to be very small in the large ’t Hooft coupling limit, and our model offers a better systematic approach to dynamics of such baryons at short distances. We compute energetics and spectra (k = 1), and also short-distance nuclear force (k = 2). In particular, we obtain a new size of the holographic baryon and find a precise form of the repulsive core of nucleons. This matrix model complements the instanton soliton picture of holographic baryons, whose small size turned out to be well below the natural length scale of the approximation involved there. Our results show that, nevertheless, the basic properties of holographic baryons obtained there are robust under stringy corrections within a few percents.

Towards the lattice effects on the holographic superconductor

A bstractWe study the lattice effects on the simple holographic toy model; massive U(1) gauge theory for the bulk action. The mass term is for the U(1) gauge symmetry breaking in the bulk. Without the lattice, the AC conductivity of this model shows similar results to the holographic superconductor with the energy gap. On this model, we introduce the lattice effects, which induce the periodic potential and break the translational invariance of the boundary field theory. Without the lattice, due to the translational invariance and the mass term, there is a delta function peak at zero frequency on the AC conductivity. We study how this delta function peak is influenced by the lattice effects, which we introduce perturbatively. In the probe limit, we evaluate the perturbative corrections to the conductivities at very small frequency limit. We find that the delta function peak remains, even after the lattice effects are introduced, although its weight reduces perturbatively. We also study the lattice wavenumber dependence of this weight. Our result suggests that in the U(1) symmetry breaking phase, the delta function peak is stable against the lattice effects at least perturbatively.

Three-body nuclear forces from a matrix model

We compute three-body nuclear forces at short distances by using the nuclear matrix model of holographic QCD proposed in our previous paper with P. Yi. We find that the three-body forces at short distances are repulsive for (a) aligned three neutrons with averaged spins, and (b) aligned proton-proton-neutron/ proton-neutron-neutron. These indicate that in dense states of neutrons such as cores of neutron stars, or in Helium3/ tritium nucleus, the repulsive forces are larger than the ones estimated from two-body forces only.

A comment on holographic Luttinger theorem

A bstractRobustness of the Luttinger theorem for fermionic liquids is examined in holography. The statement of the Luttinger theorem, the equality between the fermion charge density and the volume enclosed by the Fermi surface, can be mapped to a Gauss’s law in the gravity dual, a la Sachdev. We show that various deformations in the gravity dual, such as inclusion of magnetic fields, a parity-violating θ-term, dilatonic deformations, and higher-derivative corrections, do not violate the holographic derivation of the Luttinger theorem, as long as the theory is in a confining phase. Therefore a robustness of the theorem is found for strongly correlated fermions coupled with strongly coupled sectors which admit gravity duals. On the other hand, in the deconfined phase, we also show that the deficit appearing in the Luttinger theorem is again universal. It measures a total deficit which measures the charge of the deconfined (“fractionalized”) fermions, independent of the deformation parameters.

Three-flavor quark mass dependence of baryon spectra in holographic QCD

Abstract We introduce the strange quark mass to the Sakai–Sugimoto model of holographic QCD. We compute mass shifts in the spectra of three-flavor baryons at the leading order in perturbation in quark masses. Comparison with experimental data shows an agreement only qualitatively.