Defect a-theorem and a-maximization

• Published in: The journal of high energy physics Vol. 2022; no. 2; pp. 61 - 46
• Main Author: Wang, Yifan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022; Springer Nature B.V; SpringerOpen
• Subjects: Anomalies; Anomalies in Field and String Theories; Boundary Quantum Field Theory; Classical and Quantum Gravitation; Conformal Field Theory; Defects; Elementary Particles; Field theory; High energy physics; Maximization; Operators (mathematics); Optimization; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Subgroups; Supersymmetric Gauge Theory; Supersymmetry; Symmetry; Theorems; Boundary Quantum Field Theory; Anomalies in Field and String Theories; Conformal Field Theory; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2022)061

A bstract Conformal defects describe the universal behaviors of a conformal field theory (CFT) in the presence of a boundary or more general impurities. The coupled critical system is characterized by new conformal anomalies which are analogous to, and generalize those of standalone CFTs. Here we study the conformal a - and c -anomalies of four dimensional defects in CFTs of general spacetime dimensions greater than four. We prove that under unitary defect renormalization group (RG) flows, the defect a -anomaly must decrease, thus establishing the defect a -theorem. For conformal defects preserving minimal supersymmetry, the full defect symmetry contains a distinguished U(1) R subgroup. We derive the anomaly multiplet relations that express the defect a - and c -anomalies in terms of the defect (mixed) ’t Hooft anomalies for this U(1) R symmetry. Once the U(1) R symmetry is identified using the defect a -maximization principle which we prove, this enables a non-perturbative pathway to the conformal anomalies of strongly coupled defects. We illustrate our methods by discussing a number of examples including boundaries in five dimensions and codimension-two defects in six dimensions. We also comment on chiral algebra sectors of defect operator algebras and potential conformal collider bounds on defect anomalies.