12:45
The central charges “c” and “a” in two and four dimensional conformal field theories (CFTs) have a central organizing role in our understanding of quantum field theory (QFT) more generally. Appearing as coefficients of curvature invariants in the anomalous trace of the stress tensor, they constrain the possible relationships between QFTs under renormalization group flow. They provide important checks for dualities between different CFTs. They even have an important connection to a measure of quantum entanglement, the entanglement entropy. Less well known is that additional central charges appear when there is a boundary, four new coefficients in total in three and four dimensional boundary CFTs. While largely unstudied, these boundary charges hold out the tantalizing possibility of being as important in the classification of quantum field theory as the bulk central charges “a” and “c”. I will show how these charges can be computed from displacement operator correlation functions. I will also demonstrate a boundary conformal field theory in four dimensions with an exactly marginal coupling where these boundary charges depend on the marginal coupling. The talk is based on arXiv:1707.06224, arXiv:1709.07431, as well as work to appear shortly.