Introduction to String Theory

We give a pedagogical introduction to string theory, D-branes and p-brane solutions. 1 Introductory remarks These notes are based on lectures given at the 271-th WE-Haereus-Seminar ‘Aspects of Quantum Gravity’. Their aim is to give an introduction to string theory for students and interested researches. No previous knowledge of string theory is assumed. The focus is on gravitational aspects and we explain in some detail how gravity is described in string theory in terms of the graviton excitation of the string and through background gravitational fields. We include Dirichlet boundary conditions and D-branes from the beginning and devote one section to p-brane solutions and their relation to D-branes. In the final section we briefly indicate how string theory fits into the larger picture of M-theory and mention some of the more recent developments, like brane world scenarios. The WE-Haereus-Seminar ‘Aspects of Quantum Gravity’ covered both main approaches to quantum gravity: string theory and canonical quantum gravity. Both are complementary in many respects. While the canonical approach stresses background independence and provides a non-perturbative framework, the cornerstone of string theory still is perturbation theory in a fixed background geometry. Another difference is that in the canonical approach gravity and other interactions are independent from each other, while string theory automatically is a unified theory of gravity, other interactions and matter. There is a single dimensionful constant and all couplings are functions of this constant and of vacuum expectation values of scalars. The matter content is uniquely fixed by the symmetries of the underlying string theory. Moreover, when formulating the theory in Minkowski space, the number of space-time dimensions is fixed. As we will see, there are only five distinct supersymmetric string theories in tendimensional Minkowski space. The most important feature of string perturbation theory is the absence of UV divergencies. This allows one to compute quantum corrections to scattering amplitudes and to the effective action, including gravitational effects. More recently, significant progress has been made in understanding non-perturbative aspects of the theory, through the study of solitons and instantons, and through string dualities which map the strong coupling behaviour of one string theory to the weak coupling behaviour of a dual theory. Moreover, string dualities relate