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.
