Defect partition function from TDLs in commutant pairs

Abstract

In this paper, we study topological defect lines in two character rational conformal field theories. Among them one set of two character theories are commutant pairs in [Formula: see text] conformal field theory. Using these defect lines, we construct defect partition function in the [Formula: see text] theory. We find that the defects preserve only a part of the [Formula: see text] current algebra symmetry. We also determine the defect partition function in [Formula: see text] CFTs using these defects lines of two character theories and we find that, with appropriate choice of commutant pairs, these defects preserve all current algebra symmetries of [Formula: see text] CFTs.