A walk through superstring theory with an application to Yang-Mills theory: k-strings and D-branes as gauge/gravity dual objects

Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put forth toward this goal. A set of specific tools which are used are gauge/gravity dualities. This thesis consists of a specific implementation of gauge/gravity dualities to describe k-strings of strongly coupled gauge theories as objects dual to Dpbranes embedded in confining supergravity backgrounds from low energy superstring field theory.

Along with superstring theory, k-strings are also commonly investigated with lattice gauge theory and Hamiltonian methods. A k$string is a colorless combination of quark-anti-quark source pairs, between which a color flux tube develops. The two most notable terms of the k-string energy are, for large quark anti-quark separation L, the tension term, proportional to L, and the Coulombic 1/L correction, known as the Luscher term.

This thesis provides an overview of superstring theories and how gauge/gravity dualities emerge from them. It shows in detail how these dualities can be used for the specific problem of calculating the k-string energy in 2+1 and 3+1 space-time dimensions as the energy of Dp-branes in the dual gravitational theory. A detailed review of k-string tension calculations is given where good agreement is found with lattice gauge theory and Hamiltonian methods. In reviewing the k-string tension, we also touch on how different representations of k-strings can be described with Dp-branes through gauge/gravity dualities. The main result of this thesis is how the Luscher term is found to emerge from the energy calculation of Dp-branes. In 2+1 space-time dimensions, we have Luscher term data to compare with from lattice gauge theory, where we find good agreement.