Defect Partition Function from TDLs in Commutant Pairs

TL;DR

This paper explores topological defect lines in rational conformal field theories, constructing defect partition functions in $E_8$ and $c=24$ CFTs, revealing symmetry preservation properties of these defects.

Contribution

It introduces a method to construct defect partition functions using defect lines in two character rational CFTs, especially in commutant pairs within $E_{8,1}$.

Findings

Defects preserve partial $E_8$ symmetry in $E_8$ theory.

Defects can preserve all current algebra symmetries in certain $c=24$ CFTs.

Constructed defect partition functions provide insights into symmetry 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.