Defect Partition Function from TDLs in Commutant Pairs

TL;DR

This work classifies and constructs topological defect lines in two-character RCFTs, focusing on commutant pairs embedded in the $E_{8,1}$ theory and, via a replacement-rule method, their manifestation as defect partition functions in $E_8$ and in $c=24$ meromorphic CFTs. The authors show that defects arising from MMS commutants generally preserve only a portion of the ambient current algebra in $E_{8,1}$, while suitably chosen commutant pairs in $c=24$ theories preserve the full current algebra symmetry, with defect spectra read from modular data. The results are interpreted in group-theoretic terms through branching rules and center actions, and extended to multiple MMS pairs in several explicit examples, including $A_{1,1}$, $A_{2,1}$, $G_{2,1}$, and $D_{4,1}$. The work also connects these defect constructions to the Schellekens classification of $c=24$ meromorphic CFTs and highlights potential generalizations to higher-character RCFTs and deeper current-algebra structures.

Abstract

We study topological defect lines in two character rational conformal field theories. Among them one set of two character theories are commutant pairs in $E_{8,1}$ conformal field theory. Using these defect lines we construct defect partition function in the $E_8$ theory. We find that the defects preserve only a part of the $E_8$ current algebra symmetry. We also determine the defect partition function in $c=24$ CFTs using these defects lines of 2 character theories and we find that, with appropriate choice of commutant pairs, these defects preserve all current algebra symmetries of c = 24 CFTs.