Aspects of SUSY CFTs and RG flows

Supersymmetry is used to explore aspects of quantum field theories in various spacetime dimensions. There are interacting, supersymmetric conformal field theories (SCFTs) in six and lower spacetime dimensions. We have argued for the a-theorem in six dimensions, by using susy to connect the conformal a-anomaly to the six-dimensional analog of 't Hooft anomalies, for the R-symmetry and gravity. We also use strong constraints on the unitary representations of the superconformal group to classify supersymmetry preserving deformations of SCFTs in various spacetime dimensions.