String Scattering Amplitudes and Low Energy Effective Field Theory
To relate string theory to the usual description of particles and their interactions in terms of quantum field theories, it is important to have tools at hand to derive the effective point particle interactions for the massless excitation modes of the string. Such effective actions can be deduced from on-shell string scattering amplitudes which are computed as correlation functions of physical state vertex operators. We construct the vertex operators and compute various three-point functions which are needed to extract e.g. the interactions of graviton, two-form, dilaton and of gauge fields at leading order. We also compute the four-point functions of open and closed string tachyons and discuss some of their properties. Often the leading order (in α′) effective actions are already uniquely determined by symmetries, such as gauge symmetries or supersymmetry. We present the bosonic sectors of the ten-dimensional supergravity theories which are related to the ten-dimensional superstring theories. We also include a discussion of eleven-dimensional supergravity. The Dirac-Born-Infeld action, which governs the dynamics of the gauge field on a D-brane, will also be discussed.