#### Year of Publication

2012

#### Degree Name

Doctor of Philosophy (PhD)

#### Document Type

Doctoral Dissertation

#### College

Arts and Sciences

#### Department

Physics and Astronomy

#### First Advisor

Dr. Sumit R. Das

#### Abstract

One of the phenomenal results emerging from string theory is the A*dS*/CFT correspondence or gauge-gravity duality: In certain cases a theory of gravity is equivalent to a "dual" gauge theory, very similar to the one describing non-gravitational interactions of fundamental subatomic particles. A difficult problem on one side can be mapped to a simpler and solvable problem on the other side using this correspondence. Thus one of the theories can be understood better using the other.

The mapping between theories of gravity and gauge theories has led to new approaches to building models of particle physics from string theory. One of the important features to model is the phenomenon of confinement present in strong interaction of particle physics. This feature is not present in the gauge theory arising in the simplest of the examples of the duality. However this *N* = 4 supersymmetric Yang-Mills gauge theory enjoys the property of being integrable, i.e. it can be exactly solved in terms of conserved charges. It is expected that if a more realistic theory turns out to be integrable, solvability of the theory would lead to simple analytical expressions for quantities like masses of the hadrons in the theory. In this thesis we show that the existing models of confinement are all *nonintegrable--*such simple analytic expressions cannot be obtained.

We moreover show that these nonintegrable systems also exhibit features of chaotic dynamical systems, namely, sensitivity to initial conditions and a typical route of transition to chaos. We proceed to study the quantum mechanics of these systems and check whether their properties match those of chaotic quantum systems. Interestingly, the distribution of the spacing of meson excitations measured in the laboratory have been found to match with level-spacing distribution of typical quantum chaotic systems. We find agreement of this distribution with models of confining strong interactions, conforming these as viable models of particle physics arising from string theory.

#### Recommended Citation

Ghosh, Archisman, "TIME-DEPENDENT SYSTEMS AND CHAOS IN STRING THEORY" (2012). *Theses and Dissertations--Physics and Astronomy*. 9.

https://uknowledge.uky.edu/physastron_etds/9