Abstract: 'Chiral Perturbation Theory in Heavy Ion Collisions: transport coefficients and resonances'.

We review our general perturbative scheme for the calculation of transport coefficients of physical interest, namely, electrical and thermal conductivities and shear and bulk viscosities. We provide a consistent low-$T$ description and we show that unitarity plays a crucial role in order to reproduce the expected behaviour as $T$ approaches the chiral transition. Special attention is paid to phenomenological applications in Heavy Ion Physics, such as elliptic flow or photon spectra, as well as to more formal issues such as Ads/CFT bounds or the chiral restoration behavior. We will also review our recent work on scalar and vector resonances at finite temperature and density in the context of unitarized chiral perturbation theory and pion scattering poles, stressing chiral symmetry restoration aspects and physical applications. In particular, we describe the $sigma$/$f_0(600)$ nature as the system is driven towards chiral restoration, in connection with chiral partner degeneracy and related observed phenomena such as threshold enhancement in $pipi$ production in the nuclear medium. In the vector channel, our results for the $rho(770)$ pole are compared with different approaches aiming to describe dilepton data. We get consistency with broadening scenarios at finite temperature, whereas pure finite density chiral restoring effects could favor a scaling dropping-mass behaviour. Some papers where we discuss in depth these topics: - D. Fernandez-Fraile and A. Gomez Nicola, Int. J. Mod. Phys. E 16, 3010 (2007). - D. Fernandez-Fraile, A. Gomez Nicola, and E. T. Herruzo, Phys. Rev. D 76, 085020 (2007). - D. Fernandez-Fraile and A. Gomez Nicola, Phys. Rev. D 73, 045025 (2006). - D. Fernandez-Fraile and A. Gomez Nicola, Eur.Phys.J.A31, 848-850 (2007).