We discuss inhomogeneous ground states of the Nambu-Jona-Lasinio and quark-meson model within mean-field approximation and their possible existence in the respective phase diagrams. For this purpose we focus on lower-dimensional modulations and point out that known solutions in the 2 þ 1 and 1 þ 1 dimensional (chiral) Gross-Neveu model can be lifted to the to the 3 þ 1 dimensional Nambu-JonaLasinio model. This is worked out in detail for one-dimensional modulations and numerical results for the phase diagrams are presented. Focus is put on the critical point and on vanishing temperatures. As an interesting result the first order transition line in the phase diagram of homogeneous phases gets replaced by an inhomogeneous phase which is bordered by two second order transition lines.

We argue that there exist simple effective field theories describing the long-distance dynamics of holographic liquids. The degrees of freedom responsible for the transport of charge and energy-momentum are Goldstone modes. These modes are coupled to a strongly coupled infrared sector through emergent gauge and gravitational fields.The IR degrees of freedom are described holographically by the near-horizon part of the metric, while the Goldstone bosons are described by a field-theoretical Lagrangian. In the cases where the holographic dual involves a black hole, this picture allows for a direct connection between the holographic prescription where currents live on the boundary, and the membrane paradigm where currents live on the horizon. The zero-temperature sound mode in the D3-D7 system is also re-analyzed and re-interpreted within this formalism.

We explore the phase diagram of NJL-type models near the chiral critical point allowing for phases with spatially inhomogeneous chiral condensates. In the chiral limit it turns out that the region in the mean-field phase diagram where those phases are energetically preferred very generically reaches out to the chiral critical point. The preferred inhomogeneous ground state in this vicinity possibly resembles a lattice of domain wall solitons. This raises the question of their relevance for the phase diagram of QCD.

Using gauge/gravity duality, we compute the energy density and angular distribution of the power radiated by a quark undergoing circular motion in strongly coupled N = 4 supersymmetric YangMills (SYM) theory. We compare the strong coupling results to those at weak coupling, and find the same angular distribution of radiated power, up to an overall prefactor. In both regimes, the angular distribution is in fact similar to that of synchrotron radiation produced by an electron in circular motion in classical electrodynamics: the quark emits radiation in a narrow beam along its velocity vector with a characteristic opening angle α ∼ 1/γ. To an observer far away from the quark, the emitted radiation appears as a short periodic burst, just like the light from a lighthouse does to a ship at sea. Our strong coupling results are valid for any strongly coupled conformal field theory with a dual classical gravity description.

We investigate the role of the isoscalar-vector interaction and the dynamics of the Polyakov loop on inhomogeneous phases in the phase diagram of the two-flavor Nambu-Jona-Lasinio model. Thereby we concentrate on inhomogeneous phases with a one-dimensional modulation, explicitly domain-wall solitons and, for comparison, the chiral spiral. While the inclusion of the Polyakov loop merely leads to quantitative changes compared to the original Nambu-Jona-Lasinio model, the inclusion of a repulsive vector-channel interaction has significant qualitative effects: Whereas for homogeneous phases the firstorder phase transition gets weakened and eventually turns into a second-order transition or a crossover, the domain of inhomogeneous phases is less affected. In particular the location of the Lifshitz point in terms of temperature and density is not modified. Consequently, the critical point disappears from the phase diagram and only a Lifshitz point (showing a different critical behavior) remains. In particular, susceptibilities remain finite.