Strongly coupled non-Abelian plasmas in a magnetic field

Abstract: In this dissertation we use the gauge/gravity duality approach to study the dynamics of strongly coupled non-Abelian plasmas. Ultimately, we want to understand the properties of the quark-gluon plasma (QGP), whose scientifc interest by the scientific community escalated exponentially after its discovery in the 2000's through the collision of ultrarelativistic heavy ions. One can enrich the dynamics of the QGP by adding an external field, such as the baryon chemical potential (needed to study the QCD phase diagram), or a magnetic field. In this dissertation, we choose to investigate the magnetic effects. Indeed, there are compelling evidences that strong magnetic fields of the order $eB\sim 10 m_\pi^2$ are created in the early stages of ultrarelativistic heavy ion collisions. The chosen observable to scan possible effects of the magnetic field on the QGP was the viscosity, due to the famous result $\eta/s=1/4\pi$ obtained via holography. In a first approach we use a caricature of the QGP, the $\mathcal{N}=4$ super Yang-Mills plasma to calculate the deviations of the viscosity as we add a magnetic field. We must emphasize, though, that a magnetized plasma has a priori seven viscosity coefficients (five shears and two bulks). In addition, we also study in this same model the anisotropic heavy quark-antiquark potential in the presence of a magnetic field. In the end, we propose a phenomenological holographic QCD-like model, which is built upon the lattice QCD data, to study the thermodynamics and the viscosity of the QGP with an external strong magnetic field.