I will present a proof for a monotonicity theorem, or c-theorem, for a three-dimensional Conformal Field Theory (CFT) on a space with a boundary, and for a higher-dimensional CFT with a two-dimensional defect. The proof is applicable only to renormalization group flows that preserve locality, reflection positivity, and Euclidean invariance along the boundary or defect, are that localized at the boundary or defect, such that the bulk theory remains conformal along the flow. The method of proof is a generalization of Komargodski’s proof of Zamolodchikov’s c-theorem. The key ingredient is an external “dilaton” field introduced to match Weyl anomalies between the ultra-violet (UV) and infra-red (IR) fixed points. Reflection positivity in the dilaton’s effective action guarantees that a certain coefficient in the boundary/defect Weyl anomaly must take a value in the UV that is larger than (or equal to) the value in the IR. This boundary/defect c-theorem may have important implications for many theoretical and experimental systems, ranging from graphene to branes in string theory and M-theory.
University of Southampton
Friday, October 16, 2015 - 13:00
A Monotonicity Theorem for Two-dimensional Boundaries and Defects