Relative anomaly in (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>)d rational conformal field theory
Meng Cheng, Dominic J. Williamson
Abstract
We study 't Hooft anomalies of symmetry-enriched rational conformal field theories (RCFT) in (1 + 1)d. Such anomalies determine whether a theory can be realized in a truly (1 + 1)d system with on-site symmetry, or on the edge of a (2 + 1)d symmetry-protected topological phase. RCFTs with the identical symmetry actions on their chiral algebras may have different 't Hooft anomalies due to additional symmetry charges on local primary operators. To compute the relative anomaly, we establish a precise correspondence between (1 + 1)d nonchiral RCFTs and (2 + 1)d doubled symmetry-enriched topological (SET) phases with a choice of a symmetric gapped boundary. Based on these results we derive a general formula for the relative 't Hooft anomaly in terms of algebraic data that characterizes the SET phase and its boundary.