Effect of backreaction on holographic entanglement, chaos and page curve

Abstract

In this thesis, we primarily investigate the entanglement structure and scrambling of quantum information in the quark cloud model, which is essentially a large NV, strongly coupled thermal gauge theory backreacted by a large number (Ny) of uniformly distributed heavy fundamental quarks. The corresponding holographic gravity dual is the string cloud model, consisting of non-interacting, long fundamental strings uniformly distributed in Anti-de Sitter (AdS) black hole spacetime. Each string is oriented along the holographic radial direction, stretching from the conformal boundary to the horizon of the blackhole. The backreaction imparted by the uniform distribution of strings on the AdS blackhole geometry is exactly computable. With this holographic setup, in this thesis, we examine the effect of backreaction on various entanglement measures such as entanglement entropy (EE) and entanglement of purification(EoP) in the quark cloud model by computing the proper holographic duals, namely, the holographic entanglement entropy (HEE) and the entanglement wedge cross section (EWCS) respectively in the deformed AdS black hole. We also study the effect of backreaction on the subregion volume complexity by following the holographic complexity equals volume conjecture. We investigate the signature of chaos in the quark cloud model and study the impact of backreaction on various diagnostic parameters, e.g., Lyapunov exponent, butterfly velocity, and entanglement velocity. Further, we consider a thermofield double state within the quark cloud model with a dual gravity description, such as the deformed eternal AdS black hole with two casually disconnected asymptotic boundaries. We analyze the two-sided correlation of the TFD state by computing an appropriate measure known as holographic thermomutual information (HTMI) in the dual eternal deformed AdS black hole. We also examine the degradation of HTMI due to the presence of shockwave in eternal AdS black hole spacetime. Lastly, by determining the entanglement entropy of Hawking radiation emitted by the deformed eternal AdS black hole we analyze the effect of the backreaction on various aspects of Page curve. In our analysis. we find that, due to the presence of backreaction, the entanglement structure of the theory changes significantly. In particular,we observe that the HEE, EWCS, HTMI, and the subregion volume complexity increase with the backreaction. In our study of chaos, we notice that as the backreaction increases, the Lyapunov exponent and butterfly velocity decrease, indicating the enhancement of chaotic behavior in the system. The rate of disruption of HTMI in the presence of shockwave also increases with the backreaction parameter. Furthermore, in our analysis, we find that introducing backreaction delays the appearance of the island and modifies the Page curve, and as a consequence of that, the Page time shifts to a higher value.