Abstract
Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We provide a general derivation by comparing the trace anomaly with scale dependent contact terms in the correlation functions. We conjecture a relation between the a-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. We check our results for several free theories.
Highlights
There is a strong argument for considering, from an abstract point of view, boundaries in quantum field theory (QFT)
Boundary effects can be seen as a unifying theme in several areas where there has been enormous progress in theoretical physics
It seems reasonable that boundary conformal field theories should play a central role in the study of QFT with a boundary
Summary
Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in threeand four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We conjecture a relation between the a-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. Conformal field theories (CFTs) play a central role in QFT as fixed points of the renormalization group flow. In the presence of a boundary, there are anomalies localized on the boundary, in both odd and even dimensions These new anomalies have rich geometric structure and they introduce new central charges that could be used to characterize the theories. In d 1⁄4 3 spacetime dimensions with a two-dimensional boundary, the anomaly only appears on the boundary, and it is given by [7]
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