A Walk Through Superstring Theory With an Application to Yang-Mills Theory: K-strings and D-branes as Gauge/Gravity Dual Objects

TL;DR

This paper applies gauge/gravity dualities from superstring theory to analyze k-strings in strongly coupled gauge theories, showing how Dp-branes can model these objects and reproducing known lattice results for the Luscher term.

Contribution

It demonstrates the use of superstring gauge/gravity dualities to compute k-string energies and Luscher terms, aligning with lattice gauge theory findings.

Findings

Good agreement with lattice gauge theory for Luscher term in 2+1 dimensions

K-string energies modeled as Dp-branes in confining supergravity backgrounds

Luscher term emerges as one-loop quantum correction to Dp-brane energy

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 toward this goal. A set of specific tools which are used in this effort 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 Dp-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-antiquark 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 as the one loop quantum corrections to the Dp-brane energy. In 2+1 space-time dimensions, we have Luscher term data to compare with from lattice gauge theory, where we find good agreement.