Radial coordinates for defect CFTs

• Main Authors: Edoardo Lauria, Marco Meineri, Emilio Trevisani
• Format: Article
• Language: English
• Published: SpringerOpen 2018-11-01
• Series: Journal of High Energy Physics
• Subjects: Conformal Field Theory; Wilson, ’t Hooft and Polyakov loops; Field Theories in Higher Dimensions; Boundary Quantum Field Theory
• Online Access: http://link.springer.com/article/10.1007/JHEP11(2018)148

Abstract We study the two-point function of local operators in the presence of a defect in a generic conformal field theory. We define two pairs of cross ratios, which are convenient in the analysis of the OPE in the bulk and defect channel respectively. The new coordinates have a simple geometric interpretation, which can be exploited to efficiently compute conformal blocks in a power expansion. We illustrate this fact in the case of scalar external operators. We also elucidate the convergence properties of the bulk and defect OPE decompositions of the two-point function. In particular, we remark that the expansion of the two-point function in powers of the new cross ratios converges everywhere, a property not shared by the cross ratios customarily used in defect CFT. We comment on the crucial relevance of this fact for the numerical bootstrap.