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We investigate spatially inhomogeneous solutions in a top-down holographic model: the D3/D7 model which provides a holographic description of the chiral phase transition for a finite external magnetic field, chemical potential, and temperature. We numerically find a domain wall (or kink) solution in the three dimensional space, which incorporates between the chiral symmetry broken phase at the spatial infinity, under the homogeneous sources. Along with the inhomogeneity of the chiral condensate, the charge density is also spatially modulated. The modulated charge density and finite magnetic field lead to the chiral edge current close to the domain wall. We explore the dependences of those profiles on the chemical potential and temperature near the first and second order phase transition points. Our results indicate that the inhomogeneous solutions we found are in good agreement with those obtained by the Ginzburg-Landau theory in the vicinity of the transition points. [ABSTRACT FROM AUTHOR]

We study critical phenomena at a tricritical point associated with a chiral phase transition which emerges in the D3/D7 model in the presence of a finite baryon number density and an external magnetic field. We numerically determine critical exponents related to the thermodynamic quantities and correlation functions. We find that the values of the critical exponents agree with the mean-field values. The scaling relations between the critical exponents are satisfied, implying that the scaling hypothesis for the free energy and the correlation functions hold. Our results indicate that the critical phenomena at the tricritical point in the D3/D7 model are well described by the conventional Landau theory. [ABSTRACT FROM AUTHOR]

We investigate dispersion relation of Nambu-Goldstone modes in a dissipative system realized by the AdS/CFT correspondence. We employ the D3/D7 model which represents N = 4 supersymmetric Yang-Mills theory coupled to N = 2 flavor fields. If we consider massless quarks in the presence of an external magnetic field, the system exhibits the phase transition associated with the spontaneous symmetry breaking of the chiral symmetry. We find that the Nambu-Goldstone modes show a diffusive behavior in the dispersion relation, which agrees with that found with the effective field theory approach. We also study a non-equilibrium steady state which has a constant current flow in the presence of an external electric field. In a non-equilibrium steady state, we find that the Nambu-Goldstone modes show a linear dispersion in the real part of the frequency in addition to the diffusive behavior. Moreover, we analyze the linear dispersion of the Nambu-Goldstone modes in the hydrodynamic approximation. As a result, we find that the linear dispersion can be written as the analytic functions of quantities in the dual field theory. Our results imply that such a linear dispersion is a characteristic behavior of Nambu-Goldstone modes in a non-equilibrium steady state. [ABSTRACT FROM AUTHOR]

The theory of superconductivity can be divided into two groups depending on whether it has multi-kink solutions. For example, the BCS theory and the Gross-Neveu model have metastable multi-kink solutions whereas the conventional Ginzburg-Landau theory without higher-derivative interactions does not have any multi-kink solutions. In this paper, we systematically examine the solutions of the holographic superconductor model to find out which group the model falls into. We show that the holographic superconductor model has metastable multi-kink solutions. In this sense, we find that the holographic superconductor model falls into the category of the BCS theory and the Gross- Neveu model. We also find that the holographic superconductor model has kink crystalline condensates which are well-fitted by the Jacobi elliptic functions. [ABSTRACT FROM AUTHOR]

We study the meson spectrum of the N = 4 supersymmetric Yang-Mills theory with N = 2 fundamental hypermultiplets for a finite electric field by using the D3/D7 model. The spectrum for scalar and vector mesons is computed by analyzing the (quasi-)normal modes for the fluctuations of the D7-brane embedding and gauge fields. In the presence of an electric field, two different phases in the background are realized: the meson and dissociation phases. In this paper, we analyze the meson spectrum of scalar and vector mesons for all ranges of the electric field and explore the effect of the electric field on the meson spectrum, that is, the Stark effect. In the meson spectrum, we observe the avoided crossing between different levels due to the coupling of fluctuations via the electric field. [ABSTRACT FROM AUTHOR]

We study phase transitions and critical phenomena in nonequilibrium steady states controlled by an electric field. We employ the D3/D7 model in the presence of a charge density and electric field at finite temperatures. The system undergoes the first-order and the second-order phase transitions under the variation of the electric field in the presence of dissipation. We numerically find that the critical exponents which we define for the nonequilibrium phase transition in this model take the mean-field values. [ABSTRACT FROM AUTHOR]

We study phase transitions and critical phenomena in nonequilibrium steady states controlled by an electric field. We employ the D3/D7 model in the presence of a charge density and electric field at finite temperatures. The system undergoes the first-order and the second-order phase transitions under the variation of the electric field in the presence of dissipation. We numerically find that the critical exponents which we define for the nonequilibrium phase transition in this model take the mean-field values. [ABSTRACT FROM AUTHOR]