Final Report Summary - HOLOLHC (Holography for the LHC era) We have gained invaluable insights about the out-of-equilbrium dynamics of the quark-gluon plasma and the thermalization process by simulating heavy ion collisions as collisions of gravitational shock waves in a dual string background. We have uncovered a new relaxation channel and coined a name for it, “EoSsization”, which is now used in the heavy ions community. We have incorporated confinement and a dynamical baryon charge for the first time. We have performed the first dynamical evolution of a spinodal instability associated to a first-order phase transition and shown that both the evolution and the final, inhomogeneous state are well described by second-order hydrodynamics. We have discovered that, in collisions in theories with a first-order phase transition, a long-lived, quasi-static state may be formed. This has potentially far-reaching consequences for heavy ion collisions at the Relativistic Heavy Ion Collider that are exploring part of the rich phase diagram of Quantum Chromodynamics (QCD). A holographic model of QCD at non-zero baryon density must include three ingredients: A set of `color’ D-branes dual to the gauge group, a set of `flavor’ D-branes dual to the dynamical quarks, and a set of strings dual to the quark density. We have constructed the first and only model that incorporates the backreaction of all three ingredients, which is indispensable in order to identify the correct ground state of the system. We have also found strong indications that quark-matter crystal and color superconducting phases exist in these holographic models. The recent discovery of the gravitational wave signal from a neutron star merger opens the exciting possibility of actually testing experimentally some of the properties predicted by our holographic model. UV-incomplete theories must be thought of as effective field theories and their importance in physics can hardly be overemphasized. Quantum Electrodynamics, with its Landau pole at high energies, is a prototypical example. The Standard Model of particle physics is also thought to be in this class because of the triviality of theories with scalar fields. Although holographic duals of UV-incomplete theories were previously known, no systematic procedure to treat them existed, which was a stumbling block for the calculation of physical observables. We have provided an extremely simple solution by showing that some these holographic theories can be related, through analytic continuation in the number of dimensions, to conformal field theories, for which the calculations are understood.Finally, we have constructed theories exhibiting quasi-conformal dynamics that may capture some qualitative aspects of the physics above the electroweak scale if this physics turns out to be strongly coupled. In particular, we have determined some of the conditions necessary for the existence of a light, Higgs-like particle in the spectrum.