Anomalies in Field and String Theory
Luis Alvarez-Gaumé - CERN, Geneva
Miguel Angel Vazquez-Mozo - University of Salamanca
The course will provide an introduction to the Subject of Anomalies in Field Theory and String Theory. We will cover the classic applications in four dimensional theories concerning singlet, global and local anomalies which originated the subject. We will also cover the 't Hooft matching conditions and the 4d Witten anomaly. We will cover the subject of gauge and gravitational anomalies in diverse dimensions together with their cancellation conditions, in particular the classic ten dimensional cancellations for type IIB theories and SO(32) and E8 X E8 heterotic theories. In higher dimensions the computations will be carried out using the anomaly flow formulation which can be easily generalised to include the computation of anomalies in the presence of branes. If time permits we will provide an introduction to global anomalies.
Throughout the lectures we will provide the necessary mathematical tools: spinor algebra in arbitrary dimensions, differential topology and index theory.