Supersymmetry, branes and the mysterious M

Abstract: String theory is the only known theory that unifies general relativity and quantum mechanics in a consistent way. In recent years there has been a dramatic progress in the understanding of the non-perturbative aspects of string theory. It is now believed that string theory is part of a larger theory called M-theory. This development has been possible largely because of the rigorous constraints imposed by supersymmetry. Supersymmetric quantum field theories are interesting in their own right and might turn out to exist in a broken form in nature. Also, by studying supersymmetric field theories, an understanding of non-perturbative effects innon-supersymmetric theories can be obtained. In particular some models with N = 2 supersymmetry can be solved exactly. As an application we consider how different low energy theories arising from different gauge groups can be equivalent. In five and six dimensions we investigate some consistency conditions that constrain the matter content of these theories. It is believed that all such theories are quantum field theories at a non-trivial fixed point of the renormalization group.One exciting proposal to describe M-theory is matrix theory. The conjecture says that the full M-theory can be described by a simple quantum mechanical system. We check this proposal in certain scattering computations and find agreement with the supergravity limit of M-theory. Supersymmetry turns out to be crucial for the agreement.