By using $\mathrm{AdS}/\mathrm{CFT}$, we study the critical electric field, the Schwinger pair creation rate and the potential phase diagram for the quark and antiquark in four confining supergravity backgrounds which are the Witten QCD (WQCD), the Maldacena-Nunez (MN), the Klebanov-Tseytlin (KT) and the Klebanov-Strassler (KS) models. We compare the rate of phase transition in these models and compare it also with the conformal case. We then present the phase diagrams of the entanglement entropy of a strip in these geometries and find the predicted butterfly shape in the diagrams. We found that the phase transitions have a higher rate in WQCD and KT relative to MN and KS. Finally we show the effect of turning on an additional magnetic field on the rate of pair creation by using the imaginary part of the Euler-Heisenberg effective Lagrangian. The result is increasing the parallel magnetic field would increase the pair creation rate and increasing the perpendicular magnetic field would decrease the rate.

In this work we study how entanglement of purification (EoP) and the new quantity of “complexity of purification” are related to each other using theE_P=E_Wconjecture. First, we consider two strips in the same side of a boundary and study the relationships between the entanglement of purification of this mixed state and the parameters of the system such as dimension, temperature, length of the strips and the distance between them. Next, using the same setup, we introduce two definitions for the complexity of mixed states, complexity of purification (CoP) and the interval volume (VI). We study their connections to other parameters similar to the EoP case. Then, we extend our study to more general examples of BTZ black holes solution in massive gravity, charged black holes and multipartite systems. Finally, we give various interpretations of our results using resource theories such as LOCC and also bit thread picture.

We present evidence for the connection between the potential of different fields and complexity growth rates both in conformal and confining cases. By studying different models, we also establish a strong connection between phase transitions and the discontinuities in the complexity growth rates. In the first example, for dyonic black holes that are dual to van der Waals fluids, we find a similar first-order phase transition in the behavior of the complexity growth rate. We then compare the Schwinger effect and also the behavior of complexity in the anti–de Sitter (AdS) and AdS soliton backgrounds and comment on the connection between them. Finally, in a general Gubser model of QCD, we present the connections between the potentials, entropies, speeds of sound, and complexity growth rates during crossover and first- and second-order phase transitions, and also the behavior of quasinormal modes.

Considering a model with coupled dilaton-squared curvature terms and a dilatonic potential that replace the cosmological constant, we present an analytic hyperscaling violating solution which is the generalization of Knodel and Liu [arXiv:1305.3279] for nonzero $\theta$. We show that a specific coupling between the dilaton and the squared curvature terms produces a simple logarithmic behavior for the dilaton. By imposing causality, a null energy condition, and stability constraints, we investigate the allowed regions for the parameters of this model. We then study the perturbations around ${\mathrm{AdS}}_4$ in the UV and around ${\mathrm{AdS}}_2\times {\mathbb{R}}^2$ in the IR of the Einstein-Weyl gravity that can support an intermediate hyperscaling violating solution in order to resolve the IR singularity of the metric in four dimensions.

We study the evolution of the holographic entanglement entropy (HEE) and the holographic complexity (HC) after a thermal quench in $1+1$ dimensional boundary conformal field theories dual to massive BTZ black holes. The study indicates how the graviton mass $m_g$, the charge $q$, and also the size of the boundary region $l$ determine the evolution of the HEE and HC. We find that for small $q$ and $l$, the evolutions of the HEE and the HC is a continuous function. When $q$ or $l$ is tuned larger, the discontinuity emerges, which could not observed in the neutral ${\mathrm{AdS}}_3$ backgrounds. We show that, the emergence of this discontinuity is a universal behavior in the charged massive BTZ theory. With the increase of graviton mass, on the other hand, no emergence of the discontinuity behavior for any small $q$ and $l$ could be observed. We also show that the evolution of the HEE and HC both become stable at later times, and $m_g$ speeds up reaching to the stability during the evolution of the system. Moreover, we show that $m_g$ decreases the final stable value of HEE but raises the stable value of HC. Additionally, contrary to the usual picture in the literature that the evolution of HC has only one peak, for big enough widths, we show that graviton mass could introduce two peaks during the evolution. However, for large enough charges the one peak behavior will be recovered again. We also examine the evolutions of HEE and HC growths at the early stage, which an almost linear behavior has been detected.