PIRSA:15050124

Video URL

https://pirsa.org/15050124

A Monotonicity Theorem for Two-dimensional Boundaries and Defects

O'Bannon, A. (2015). A Monotonicity Theorem for Two-dimensional Boundaries and Defects. Perimeter Institute for Theoretical Physics. https://pirsa.org/15050124

O'Bannon, Andrew. A Monotonicity Theorem for Two-dimensional Boundaries and Defects. Perimeter Institute for Theoretical Physics, May. 28, 2015, https://pirsa.org/15050124 

          @misc{ scivideos_PIRSA:15050124,
            doi = {10.48660/15050124},
            url = {https://pirsa.org/15050124},
            author = {O{\textquoteright}Bannon, Andrew},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {A Monotonicity Theorem for Two-dimensional Boundaries and Defects},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2015},
            month = {may},
            note = {PIRSA:15050124 see, \url{https://scivideos.org/index.php/pirsa/15050124}}
          }

Andrew O'Bannon University of Southampton

Talk numberPIRSA:15050124
DOI10.48660/15050124
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

I will propose 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 two-dimensional defect coupled to a higher-dimensional CFT. The proof is applicable only to renormalization group flows that are localized at the boundary or defect, such that the bulk theory remains conformal along the flow, and that preserve locality, reflection positivity, and Euclidean invariance along the defect. 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.