Strings, D-branes and Calabi-Yau compactifications

Abstract: String theories are given by 1+1 dimensional (`worldsheet') field theories, which are embedded in a 1+(D-1) dimensional `target' spacetime. Quantisation of the theory plusupersymmetry (=relation among bosonic and fermionic fields) constrains the target spacetime to be ten dimensional. Compactifications of six dimensions on Calabi-Yau threefolds lead to four dimensional supersymmetric field theories. Endpoints of open strings are confined to p-dimensional planes, the `Dp-branes', within the target spacetime and provide gauge degrees of freedom. This talk aims at providing a brief introduction into the basic concepts of string theory (and D-branes) and why Calabi-Yau manifolds (and special Lagrangian cycles) are of interest to theoretical physicists.