Open strings and analytic non-integrability

Abstract

The AdS/CFT correspondence has proved to be a powerful tool in the analysis of many systems of interest in theoretical physics. Strongly coupled gauge theories that are difficult to solve can be determined by using gravitational theory instead. Based on this concept the integrability, or rather non-integrability of a gauge theory system can be determined using semi-classical string solutions. Integrability has become a coveted property in a system. It indicates that the system can be solved fully. Since there is no systematic method to check for integrability, the analytic non-integrability method was conceived to provide a way to test for non-integrability in string theory by following a set of fixed steps. This method has been able to test for non-integrability in a variety of backgrounds containing closed string solutions. One question that remains is whether the method can be extended to include open strings. In this dissertation, the analytic non-integrability method is used to test for non- integrability for an open string solution ending on a Y = 0, maximal giant graviton. The solution that is used is the Hofman-Maldacena giant magnon. The method is also tested for open strings ending on a D5 and D7 brane. Two variations are used for the metric of the D7 brane. These are the S 2 × S 2 and the nested S 4 metrics of the S 5 . The method was able to reproduce the expected results for the D5 brane and the giant graviton. This is a strong indication that the method can be successfully adapted when checking for non-integrability in open string solutions. There is po- tential for the method to conclusively prove non-integrability in the D7 brane case if an appropriate open string solution can be found.