Central charges of 2d superconformal defects

• Published in: The journal of high energy physics 2020-05, Vol.2020 (5), p.1-52, Article 95
• Main Authors: Chalabi, Adam, O’Bannon, Andy, Robinson, Brandon, Sisti, Jacopo
• Format: Article
• Language: English
• Subjects: AdS-CFT Correspondence; Classical and Quantum Gravitation; Conformal Field Theory; Defects; Elementary Particles; High energy physics; Holography; Partitions (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Gauge Theory; Supersymmetry and Duality; Yang-Mills theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2020)095

A bstract In conformal field theories (CFTs) of dimension d > 3, two-dimensional (2d) conformal defects are characterised in part by central charges defined via the defect’s contribution to the trace anomaly. However, in general for interacting CFTs these central charges are difficult to calculate. For superconformal 2d defects in supersymmetric (SUSY) CFTs (SCFTs), we show how to compute these defect central charges from the SUSY partition function either on S d with defect along S 2 , or on S 1 × S d− 1 with defect along S 1 × S 1 . In the latter case we propose that defect central charges appear in an overall normalisation factor, as part of the SUSY Casimir energy. For 2d half-BPS defects in 4d N = 2 SCFTs and in the 6d N = (2 , 0) SCFT we obtain novel, exact results for defect central charges using existing results for partition functions computed using SUSY localisation, SUSY indices, and correspondences to 2d Liouville, Toda, and q -deformed Yang-Mills theories. Some of our results for defect central charges agree with those obtained previously via holography, showing that the latter are not just large- N and/or strong- coupling limits, but are exact. Our methods can be straightforwardly extended to other superconformal defects, of various codimension, as we demonstrate for a 4d defect in the 6d N = (2 , 0) SCFT.