Branes and applications in string theory and M-theory

Abstract

This thesis discusses branes in string theory and M-theory. In chapter 1, we present background materials. In chapters 2 and 3, we discuss an application of a D3/D7 model in the framework of gauge/gravity duality, which uses the results of a gravity theory calculation to obtain informations about the corresponding gauge theory. Gauge/gravity duality is usually studied in a non-compact space. This thesis, however, focuses on the duality in a compact space. In chapter 2, we study a strongly coupled gauge theory in a compact space. We find that a homogeneous ground state is unstable at a sufficiently large isospin chemical potential. We then construct a new ground state which corresponds to a scalar meson condensate charged under a global SO(4) symmetry. In chapter 3, we discuss an on-going work. We study a strongly-coupled gauge theory living in a compact space with a generic value of quark mass at zero temperature in the presence of an external magnetic field. We are investigating the phase diagram of the external magnetic field and quark mass.

In chapter 4 and 5, we move to M-theory. In chapter 4, we construct a complete non-linear theory of a supersymmetric single M5-brane with a 3+3 splitting. The M5-brane lives in a general background of M-theory. The idea of our construction is to get equations of motion that agree with that obtained from the superembedding approach. In chapter 5, we consider a model which attempts to describe a theory on multiple M5-branes. Using this model, we construct self-dual string solutions which describes M2/M5 branes intersection. These solutions are supported by magnetic monopoles. For self-dual strings with large number of M2 and M5-branes, we obtain the required radius-distance relationship and energy.