#### Document Type

Dissertation

#### Date of Degree

Summer 2010

#### Degree Name

PhD (Doctor of Philosophy)

#### Degree In

Physics

#### First Advisor

Vincent G. Rodgers

#### Abstract

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 D*p*branes 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 D*p*-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 D*p*-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 D*p*-branes. In 2+1 space-time dimensions, we have Luscher term data to compare with from lattice gauge theory, where we find good agreement.

#### Keywords

AdS, brane, lattice, QCD, string, strong

#### Pages

2, viii, 121

#### Bibliography

117-121

#### Copyright

Copyright 2010 Kory M Stiffler