This project explored both the mathematical and physical aspects used in studying Dirichlet branes. Dirichlet branes (D-branes) are objects that are used in string theory to help describe certain particle interactions represented by open strings. We looked at a certain 9+1 dimensional spacetime background pertaining to anti-de Sitter/quantum chromodynamic correspondence in which we place a D-brane into. It is in our best interest to simplify the mathematical representation of these objects, as doing so would allow for the particle interactions on them to be described and studied more easily. For this reason we aim to find an optimal choice of coordinate system in describing them, similarly to how it is natural to describe a circle in terms of polar coordinates.
One of our goals is to gain a better understanding of this D-brane and the underlying connections between mathematics and physics. To do this, we present on how we visualize this D-brane embedding and will explain the various mathematical tools that were used to get there from the perspective of both a mathematician and a physicist. These tools include the concept of induced metrics and action principles such as the Euler-Lagrange equation and Hamilton's equation.