Abstract:
We study the Sakai-Sugimoto model of holographic QCD at zero temperature and finite chemical potential. We find that as the baryon chemical potential is increased above a critical value, there is a phase transition to a nuclear matter phase characterized by a condensate of instantons on the probe D-branes in the string theory dual. As a result of electrostatic interactions between the instantons, this condensate expands towards the UV when the chemical potential is increased, giving a holographic version of the expansion of the Fermi surface. We argue based on properties of instantons that the nuclear matter phase is necessarily inhomogeneous to arbitrarily high density. This suggests an explanation of the "chiral density wave" instability of the quark Fermi surface in large N_c QCD at asymptotically large chemical potential. We study properties of the nuclear matter phase as a function of chemical potential beyond the transition and argue in particular that the model can be used to make a semi-quantitative prediction of the binding energy per nucleon for nuclear matter in ordinary QCD.

Abstract:
We study collective excitations of cold (2+1)-dimensional fundamental matter living on a defect of the four-dimensional N=4 super Yang-Mills theory in the Higgs branch. This system is realized holographically as a D3-D5 brane intersection, in which the D5-brane is treated as a probe with a non-zero gauge flux across the internal part of its worldvolume. We study the holographic zero sound mode in the collisionless regime at low temperature and find a simple analytic result for its dispersion relation. We also find the diffusion constant of the system in the hydrodynamic regime at higher temperature. In both cases we study the dependence on the flux parameter which determines the amount of Higgs symmetry breaking. We also discuss the anyonization of this construction.

Abstract:
In the past years a wealth of observations has unraveled the structural properties of dark and luminous mass distribution in galaxies, a benchmark for understanding dark matter and the process of galaxy formation. The study of the kinematics of over thousand spirals has evidenced a dark-luminous matter coupling and the presence of a series of scaling laws, pictured by the Universal Rotation Curve paradigm, an intriguing observational scenario not easily explained by present theories of galaxy formation.

Abstract:
We discuss superfluidity in neutron matter, with particular attention to induced interactions and to universal properties accessible with cold atoms.

Abstract:
We discuss the universal relation between density and size of observed Dark Matter halos that was recently shown to hold on a wide range of scales, from dwarf galaxies to galaxy clusters. Predictions of LambdaCDM N-body simulations are consistent with this relation. We demonstrate that this property of LambdaCDM can be understood analytically in the secondary infall model. Qualitative understanding given by this model provides a new way to predict which deviations from LambdaCDM or large-scale modifications of gravity can affect universal behavior and, therefore, to constrain them observationally.

Abstract:
In this paper I report the highlights of the talk: "Universal properties in galaxies and cored Dark Matter profiles", given at: Colloquium Lectures, Ecole Internationale d'Astrophysique Daniel Chalonge. The 14th Paris Cosmology Colloquium 2010 "The Standard Model of the Universe: Theory and Observations".

Abstract:
We study asymmetric dense matter in holographic QCD.We construct asymmetric dense matter by considering two quark flavor branes with dierent quark masses in a D4/D6/D6 model. To calculate the symmetry energy in nuclear matter, we consider two quarks with equal masses and observe that the symmetry energy increases with the total charge showing the stiff dependence. This behavior is universal in the sense that the result is independent of parameters in the model. We also study strange (or hyperon) matter with one light and one intermediate mass quarks. In addition to the vacuum properties of asymmetric matter, we calculate meson masses in asymmetric dense matter and discuss our results in the light of in-medium kaon masses.

Abstract:
We present some general considerations on the properties of a two-component ultra-cold Fermi gas along the BEC-BCS crossover. It is shown that the interaction energy and the ground state energy can be written in terms of a single dimensionless function $h({\xi,\tau})$, where $\xi=-(k_Fa_s)^{-1}$ and $\tau=T/T_F$. The function $h(\xi,\tau)$ incorporates all the many-body physics and naturally occurs in other physical quantities as well. In particular, we show that the RF-spectroscopy shift $\bar{\d\o}(\xi,\tau)$ and the molecular fraction $f_c(\xi,\tau)$ in the closed channel can be expressed in terms of $h(\xi,\tau)$ and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments.

Abstract:
In a wide class of holographic models, like the one proposed by Sakai and Sugimoto, baryons can be approximated by instantons of non-abelian gauge fields that live on the world-volume of flavor D-branes. In the leading order, those are just the Yang-Mills instantons, whose solutions can be obtained from the celebrated ADHM construction. This fact can be used to study various properties of baryons in the holographic limit. In particular, one can attempt to construct a holographic description of the cold dense nuclear matter phase of baryons. It can be argued that holographic baryons in such a regime are necessarily in a solid crystalline phase. In this review we summarize the known results on the construction and phases of crystals of the holographic baryons.

Abstract:
We present a comparison of halo properties in cosmological simulations of collisionless cold dark matter (CDM) and self-interacting dark matter (SIDM) for a range of dark matter cross sections. We find, in agreement with various authors, that CDM yields cuspy halos that are too centrally concentrated as compared to observations. Conversely, SIDM simulations using a Monte Carlo N-body technique produce halos with significantly reduced central densities and flatter cores with increasing cross section. We introduce a concentration parameter based on enclosed mass that we expect will be straightforward to determine observationally, unlike that of Navarro, Frenk & White, and provide predictions for SIDM and CDM. SIDM also produces more spherical halos than CDM, providing possibly the strongest observational test of SIDM. We discuss our findings in relation to various relevant observations as well as SIDM simulations of other groups. Taking proper account of simulation limitations, we find that a dark matter cross section per unit mass of sigma_DM ~= 10^{-23}-10^{-24} cm^2/GeV is consistent with all current observational constraints.