#### Year of Publication

2014

#### Degree Name

Doctor of Philosophy (PhD)

#### Document Type

Doctoral Dissertation

#### College

Arts and Sciences

#### Department/School/Program

Physics and Astronomy

#### First Advisor

Dr. Sumit R. Das

#### Abstract

One of the most important results emerging from string theory is the gauge gravity duality (*AdS/CFT* correspondence) which tells us that certain problems in particular gravitational backgrounds can be exactly mapped to a particular dual gauge theory a quantum theory very similar to the one explaining the interactions between fundamental subatomic particles. The chief merit of the duality is that a difficult problem in one theory can be mapped to a simpler and solvable problem in the other theory. The duality can be used both ways.

Most of the current theoretical framework is suited to study equilibrium systems, or systems where time dependence is at most adiabatic. However in the real world, systems are almost always out of equilibrium. Generically these scenarios are described by quenches, where a parameter of the theory is made time dependent. In this dissertation I describe some of the work done in the context of studying quantum quench using the AdS/CFT correspondence. We recover certain universal scaling type of behavior as the quenching is done through a quantum critical point. Another question that has been explored in the dissertation is time dependence of the gravity theory. Present cosmological observations indicate that our universe is accelerating and is described by a spacetime called de-Sitter(dS). In 2011 there had been a speculation over a possible duality between de-Sitter gravity and a particular field theory (Euclidean SP(N) CFT). However a concrete realization of this proposition was still lacking. Here we explicitly derive the *dS/CFT* duality using well known methods in field theory. We discovered that the time dimension emerges naturally in the derivation. We also describe further applications and extensions of dS/CFT.

#### Recommended Citation

Das, Diptarka, "TIME DEPENDENT HOLOGRAPHY" (2014). *Theses and Dissertations--Physics and Astronomy*. 16.

https://uknowledge.uky.edu/physastron_etds/16

#### Included in

Condensed Matter Physics Commons, Elementary Particles and Fields and String Theory Commons