CERN experiment NA60 has measured low-mass muon pair production in In-In collisions at 158 GeV/nucleon with unprecedented precision. The data is reproduced very well by a dynamical model which also describes hadron spectra and two-particle HBT correlations. The data is consistent with the properties of rho and omega vector mesons at finite temperature and density as deduced from empirical forward scattering amplitudes. In particular, these mesons have greatly broadened widths but no significant shift in mass.

The notion that the matter formed in heavy-ion collisions at RHIC has extremely low viscosity was based on the success of ideal fluid hydrodynamical models. In this talk I will review ideal fluid models used to describe heavy-ion collisions, and their uncertainties to show how large dissipative corrections to ideal model results the data actually allows. In particular I will discuss the effects of equation of state and freeze-out process. I will also briefly discuss the recent calculations applying viscous hydrodynamics to heavy-ion collisions.

Due to the short time scales of a heavy ion collision, probes created during the collision are needed. Until recently, studies of the bulk matter created in a heavy ion collision have used the abundantly produced hadrons, particularly pions. Since pions interact strongly with the medium, the information they carry is focused late in the evolution, long after the medium has cooled from a quark-gluon plasma (QGP) phase. Photons, however, decouple upon creation, and are especially focused at large temperatures like a QGP phase. Although rare, photons yield valuable possible constraints on the dynamic models used to describe the heavy ion collision. Here, I present our results for electromagnetic radiation of heavy ion collisions from ideal hydrodynamics. We explore the dynamics of a collision through both the spectra and hydrodynamic flow of photons. I will also briefly examine the possibility of exploring the geometry of the collision through photon intensity interferometry from ideal hydrodynamics.

The study of QCD at low energies is relevant in explaining the world around us but is extremely difficult due to the mathematical structure of the theory. The linear sigma model is a well known and simple effective model for low-energy QCD. We couple the O(4) linear sigma model to quark fields in order to study the effects of the quarks and mesons on the chiral phase transition as functions of the temperature T and the quark chemical potential μ_q . As an effective model for QCD, we hope to reproduce some aspects of the QCD phase diagram, namely,
the line of first order transitions that has a critical end-point at a second order transiton. We study how this line varies with changing pion mass. We use the self-consistent Cornwall-Jackiw-Tomboulis method in an extended Hartree approximation using a summation over all daisy diagrams. We study the mesonic and quark properties, including mean field, fluctuations and effective masses and how they relate to the transition structure.

AdS/CFT correspondence promises to decribe non-perturbative QCD but we have some way to go before reaching that goal. In this talk I explain recent attempts to develop an AdS/QCD model and describe numerical and analytical
to incorporate both spontaneous and explicit chiral symmetry breaking.

The study of QCD (Quantum Chromo-Dynamics) at low energies is relevant to explaining the sub-atomic world but is extremely difficult due to the mathematical structure of the theory. We use the O(4) linear sigma model with quark fields to study the chiral phase transition as a function of the temperature T and the baryon chemical potential μ_B . As an effective model for QCD, we hope to reproduce some aspects of the QCD phase diagram, namely, the line of first order phase transitions that has a critical endpoint at a second order phase transiton. We study how this line varies with changing pion mass. We use a fully self-consistent method which includes both mean fields and fluctuations. We study the mesonic and quark properties, including mean field, fluctuations and effective masses and how they relate to the transition structure.

It is well known that point transformations of a Lagrangian leave the Euler-Lagrange equations of motion unchanged. The question becomes much more difficult in the context of quantum field theory. It was first studied in the context of zero temperature field theory. It was shown that the S-matrix elements are independent of the choice of field appearing in the Lagrangian. This is equivalent to the statement that observables are invariant under a field redefinition for the fields appearing in the Lagrangian. This theorem holds for renormalizeable field theories. The case of finite temperature is much less understood. We study the difficulties of our self-consistent method in terms of field redefinitions.

Neutron stars in low-mass X-ray binaries can accrete hydrogen and helium from a companion star. This matter undergoes thermonuclear burning in the neutron star envelope. In the case of unstable burning a flash is observed: a type I X-ray burst. I will present our analyses of rare bursts: those with short recurrence times and long duration bursts which last a day (superbursts). Recently we created a multi-zone numerical model of the neutron star envelope, where we include mixing due to rotation and a rotationally induced magnetic field. I will discuss how mixing may explain the observed transition from stable to unstable burning as a function of the mass accretion rate.