Finite level geometry of fractional branes

TL;DR

This paper addresses issues in associating functions to Ishibashi states in certain CFT models with fixed points, proposing an alternative method that yields orthogonal functions in some cases.

Contribution

It introduces a new function assignment method for Ishibashi states in simple current models with fixed points, improving their mathematical properties.

Findings

Standard averaging can produce vanishing functions.

The new assignment yields orthogonal Ishibashi functions.

Applicable to specific models like SO(3) at certain levels.

Abstract

In some CFT models of simple current type, which are used to describe string theory on orbifolds and (adjoint) cosets of Lie groups, there arise fixed points of the simple current group. In these cases, the standard procedure to associate functions to Ishibashi states by averaging out the action of the simple current group, gives functions with unsatisfactory properties. In some cases the averaged Ishibashi function simply vanishes, which we see explicitly in SO(3) at level k=4l+2. In this note, an alternative function assignment is suggested, and it is shown that in some cases the resulting Ishibashi functions are orthogonal.