Investigations of Boundaries and Branes in the Holographic Duality

Quantum conformal field theory (CFT) is a special type of quantum field theory which is symmetric under conformal transformations of space-time. Because of their relative simplicity, CFTs appear in many different areas of theoretical physics such as condensed matter physics and quantum gravity. For example in the study of statistical mechanical systems, CFTs appear as continuum effective descriptions of collective phenomena near a critical point where a phase transition occurs. In this context, the existence of different types of CFTs is connected to the classification of different universality classes of phase transitions. As theories by themselves, CFTs do not describe the gravitational force which is transmitted by the graviton particle. However, CFTs are deeply connected to gravity in string theory where they determine the dynamics of quantum mechanical strings. The spectrum of vibrational modes of a string include the graviton making string theory a theory of quantum gravity which is self-consistent based on vast theoretical knowledge. Hence CFTs have played a central role in the development of string theory and in our quest to unify Einstein's theory of gravity with quantum mechanics. The main milestone in the modern understanding of quantum gravity was the discovery of the holographic duality in string theory. Simply put, the duality says that there exist special CFTs which contain rules to describe gravity hidden in them. However, these rules are holographic, because they describe gravity in a space-time with one extra dimension: the duality is like a hologram where a three-dimensional image (gravity) is encoded on a two-dimensional surface (CFT). Not only is the holographic duality useful in understanding the structure of quantum gravity, it is also extremely powerful in predicting dynamics of strongly interacting quantum fields that occur inside neutron stars for example. This thesis is devoted to the study of the holographic duality and it is based on four research articles on the topic. The focus is on how extended objects, namely boundaries and branes, behave on both sides of the duality. In string theory, boundaries of open strings describe dynamics of D-branes whose understanding was crucial for the discovery of the holographic duality in the first place. Similarly on the CFT side, boundaries give raise to observable effects such as the Casimir effect when the system is confined between two parallel plates. The goal of the thesis is to give an introduction to these concepts in the context of the holographic duality. (author)