We present the string dual to SU(N _c ) \( \mathcal{N} = 4 \) SYM, coupled to N _f massless fundamental flavors, at finite temperature and baryon density. The solution is determined by two dimensionless parameters, both depending on the ’t Hooft coupling λ _h at the scale set by the temperature T: ϵ _h ∼ λ _h N _f /N _c , weighting the backreaction of the flavor fields and \( \tilde{\delta } \sim {{{\lambda_h^{{{{ - 1}} \left/ {2} \right.}}{n_b}}} \left/ {{\left( {{N_f}{T^3}} \right)}} \right.} \), where n _b is the baryon density. For small values of these two parameters the solution is given analytically up to second order. We study the thermodynamics of the system in the canonical and grand-canonical ensembles. We then analyze the energy loss of partons moving through the plasma, computing the jet quenching parameter and studying its dependence on the baryon density. Finally, we analyze certain “optical” properties of the plasma. The whole setup is generalized to non abelian strongly coupled plasmas engineered on D3-D7 systems with D3-branes placed at the tip of a generic singular Calabi-Yau cone. In all the cases, fundamental matter fields are introduced by means of homogeneously smeared D7-branes and the flavor symmetry group is thus a product of abelian factors.

We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2 + 1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS₄. In global coordinates there exists a variety of evolutions towards final black hole formation which we relate with different patterns of relaxation in the dual field theory. For large scalar initial data rapid thermalization is achieved as a priori expected. Interesting phenomena appear for small enough amplitudes. Such shells do not generate a black hole by direct collapse, but quite generically, an apparent horizon emerges after enough bounces off the AdS boundary. We relate this bulk evolution with relaxation processes at strong coupling which delay in reaching an ergodic stage. Besides the dynamics of bulk fields, we monitor the entanglement entropy, finding that it oscillates quasi-periodically before final equilibration. The radial position of the travelling shell is brought in correspondence with the evolution of the pattern of entanglement in the dual field theory. We propose, thereafter, that the observed oscillations are the dual counterpart of the quantum revivals studied in the literature. The entanglement entropy is not only able to portrait the streaming of entangled excitations, but it is also a useful probe of interaction effects.

We study holographic models related to global quantum quenches in finite size systems. The holographic set up describes naturally a CFT, which we consider on a circle and a sphere. The enhanced symmetry of the conformal group on the circle motivates us to compare the evolution in both cases. Depending on the initial conditions, the dual geometry exhibits oscillations that we holographically interpret as revivals of the initial field theory state. On the sphere, this only happens when the energy density created by the quench is small compared to the system size. However on the circle considerably larger energy densities are compatible with revivals. Two different timescales emerge in this latter case. A collapse time, when the system appears to have dephased, and the revival time, when after rephasing the initial state is partially recovered. The ratio of these two times depends upon the initial conditions in a similar way to what is observed in some experimental setups exhibiting collapse and revivals.

We study linear and nonlinear stability of asymptotically AdS₄ solutions in Einstein-Maxwell-scalar theory. After summarizing the set of static solutions we first examine thermodynamical stability in the grand canonical ensemble and the phase transitions that occur among them. In the second part of the paper we focus on nonlinear stability in the microcanonical ensemble by evolving radial perturbations numerically. We find hints of an instability corner for vanishingly small perturbations of the same kind as the ones present in the uncharged case. Collapses are avoided, instead, if the charge and mass of the perturbations come to close the line of solitons. Finally we examine the soliton solutions. The linear spectrum of normal modes is not resonant and instability turns on at extrema of the mass curve. Linear stability extends to nonlinear stability up to some threshold for the amplitude of the perturbation. Beyond that, the soliton is destroyed and collapses to a hairy black hole. The relative width of this stability band scales down with the charge Q, and does not survive the blow up limit to a planar geometry.

We study periodically driven scalar fields and the resulting geometries with global AdS asymptotics. These solutions describe the strongly coupled dynamics of dual finite-size quantum systems under a periodic driving which we interpret as Floquet condensates. They span a continuous two-parameter space that extends the linearized solutions on AdS. We map the regions of stability in the solution space. In a significant portion of the unstable subspace, two very different endpoints are reached depending upon the sign of the perturbation. Collapse into a black hole occurs for one sign. For the opposite sign instead one attains a regular solution with periodic modulation. We also construct quenches where the driving frequency and amplitude are continuously varied. Quasistatic quenches can interpolate between pure AdS and sourced solutions with time periodic vev. By suitably choosing the quasistatic path one can obtain boson stars dual to Floquet condensates at zero driving field. We characterize the adiabaticity of the quenching processes. Besides, we speculate on the possible connections of this framework with time crystals.