Motivated by T T deformation of a conformal field theory we compute holographic complexity for a black brane solution with a cut off using "complexity=action" proposal. In order to have a late time behavior consistent with Lloyd's bound one is forced to have a cut off behind the horizon whose value is fixed by the boundary cut off. Using this result we compute holographic complexity for two dimensional AdS solutions where we get expected late times linear growth. It is in contrast with the naively computation which is done without assuming the cut off where the complexity approaches a constant at the late time.

Using a five dimensional AdS soliton in an Einstein-Yang-Mills theory with SU (2) gauge group we study p-wave holographic insulator/superconductor phase transition. To explore the phase structure of the model we consider the system in the probe limit as well as fully back reacted solutions. We will also study zero temperature limit of the p-wave holographic superconductor in four dimensions. Dedicated to the memory of Mohammad Hossein Sarmadi

We consider the Complexity=Action (CA) proposal in Einstein gravity and investigate new counterterms which are able to remove all the UV divergences of holographic complexity.We first show that the two different methods for regularizing the gravitational on-shell action proposed in [1] are completely equivalent, provided that one considers the Gibbons-Hawking-York term as well as new counterterms inspired from holographic renormalization on timelike boundaries of the WDW patch. Next, we introduce new counterterms on the null boundaries of the WDW patch for four and five dimensional asymptotically AdS spacetimes which are able to remove all the UV divergences of the on-shell action. Moreover, they are covariant and do not change the equations of motion. At the end, we calculate the null counterterms for an AdS-Schwarzschild black hole.

We study different features of 3D non-relativistic CFT using gravity description. As the corresponding gravity solution can be embedded into the type IIB string theory, we study semi-classical closed/open strings in this background. In particular we consider folded rotating and circular pulsating closed strings where we find the anomalous dimension of the dual operators as a function of their quantum numbers. We also consider moving open strings in this background which can be used to compute the drag force. In particular we find that for slowly moving particles, the energy is lost exponentially and the characteristic time is given in terms of the temperature, while for fast moving particles the energy loss goes as inverse of the time and the characteristic time is independent of the temperature.Dedicated to Reza Mansouri on the occasion of his 60th birthday