The time-scale of thermalization in holographic dual models with a chemical potential in diverse number of dimensions is systematically investigated using the gauge/gravity duality. We consider a model with a thin-shell of charged dust collapsing from the boundary toward the bulk interior of asymptotically anti-de Sitter (AdS) spaces. In the outer region there is a Reissner-Nordström-AdS black hole (RNAdS-BH), while in the inner region there is an anti-de Sitter space. We consider renormalized geodesic lengths and minimal area surfaces as probes of thermalization, which in the dual quantum field theory (QFT) correspond to two-point functions and expectation values of Wilson loops, respectively. We show how the behavior of these extensive probes changes for charged black holes in comparison with Schwarzschild-AdS black holes (AdS-BH), for different values of the black hole mass and charge. The full range of values of the chemical potential over temperature ratio in the dual QFT is investigated. In all cases, the structure of the thermalization curves shares similar features with those obtained from the AdS-BH. On the other hand, there is an important difference in comparison with the AdS-BH: the thermalization times obtained from the renormalized geodesic lengths and the minimal area surfaces are larger for the RNAdS-BH, and they increase as the black hole charge increases.

We obtain explicit realizations of holographic renormalization group (RG) flows from Mtheory, from E 2,1 × Spin(7) at UV to AdS 4 ×S 7 (squashed S 7 ) at IR, from E 2,1 × CY 4 at UV to AdS 4 × Q 1,1,1 at IR, and from E 2,1 × HK (hyperKahler) at UV to AdS 4 × N 0,1,0 at IR. The dual type IIA string theory configurations correspond to D2-D6 brane systems where D6-branes wrap supersymmetric four-cycles. We also study the Penrose limits and obtain the pp-wave backgrounds for the above configurations. Besides, we study some examples of non-supersymmetric and supersymmetric flows in five-dimensional gauge theories.

Intriguing connections to the twistorial formulation of N = 4 Yang-Mills are also noted.

We study deep inelastic scattering structure functions from hadrons using different holographic dual models which describe the strongly coupled regime of gauge theories in the large N limit. Particularly, we consider scalar and vector mesons obtained from holographic descriptions with fundamental degrees of freedom, corresponding to N = 2 supersymmetric and non-supersymmetric Yang-Mills theories. We explicitly obtain analytic expressions for the full set of eight structure functions, i.e., F 1 , F 2 , g 1 , g 2 , b 1 , b 2 , b 3 , b 4 , arising from the standard decomposition of the hadronic tensor of spin-one hadrons. We obtain the relations 2F 1 = F 2 and 2b 1 = b 2 . In addition, we find b 1 ∼ O(F 1 ) as suggested by Hoodbhoy, Jaffe and Manohar for vector mesons. Also, we find new relations among some of these structure functions.