Conformal anomalies of CFT's with boundaries

TL;DR

This paper investigates how boundaries affect the trace anomaly in four-dimensional conformal field theories, introducing new boundary-related functions and computing their values for various theories and conditions.

Contribution

It identifies and computes new boundary charges related to the trace anomaly, extending the understanding of boundary effects in 4D CFTs.

Findings

Boundary charges depend on bulk $a$ and $c$ functions.

Boundary charges vary with boundary conditions.

One boundary charge is related to the bulk $c$ charge.

Abstract

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.