Conformal anomalies of CFT's with boundaries

The trace anomaly of conformal field theories in four dimensions is characterized by ‘$a$’ and ‘$c$’-functions. The scaling properties of the effective action of a CFT in the presence of boundaries is shown to be determined by $a$, $c$ and two new functions (charges) related to boundary effects. The boundary charges are computed for different theories and different boundary conditions. One of the boundary charges depends on the bulk $c$ charge.