On Intersecting 2-Brane Solutions in Type IIA Supergravity Theory
In string theory, a string is a one-dimensional strand of energy with a size scale of 10-33 cm living in ten dimensional spacetime. Theoretically, the known subatomic particles, such as quarks and electrons, are made of strings, where their properties, such as mass and spin, are consequences of different oscillations on the string. The appeal of string theory arises from the fact that it also contains within it a quantum mechanical version of general relativity as a special case, providing for the first time the possibility of a theory of all the known interactions. Supergravity theories arise from string theory as low energy limits. They are classical theories of gravity and other types of fields. Solutions to the nonlinear Einstein and field equations of supergravity are necessarily solutions of string theory as well. Many such solutions are known as p-branes: extended objects spanning p spatial dimensions. A 0-brane is a point-like object while a 1-brane is string-like and so on. The hunt for and categorization of such solutions has been particularly popular in the literature in recent years. We are interested in a solution in type IIA supergravity that corresponds to two intersecting 2-branes coupled to a 3-form gauge potential, and a scalar field traditionally known as the dilaton. We derive the equations of motion of the theory and construct an ansatz to the solution. Other, previously known, intersecting brane solutions have provided the groundwork for further understanding the full structure of string theory and how it relates to other theories in lower dimensions. We want to know this because we want to classify as many possible solutions to string theory as are possible. Classifying these solutions may lead to understanding some cosmological applications of branes. Brane solutions may also provide us clues to understanding nonlinear theories in general. These solutions are not limited to string theory they may even lead to applications in particle physics theory as well.