Charges of Exceptionally Twisted Branes

TL;DR

This paper determines the charges of exceptionally twisted D-branes in WZW models from a microscopic/CFT perspective, confirming they match untwisted branes' charge groups and revealing surprising Lie-theoretic connections.

Contribution

It explicitly calculates the charges of twisted D-branes and proves their charge groups are identical to untwisted cases using Lie theory and CFT methods.

Findings

Twisted brane charges match untwisted brane charge groups.

Lie theory reveals G2 and F4 Weyl dimensions relate to simple currents.

Charge groups confirmed by microscopic and K-theoretic approaches.

Abstract

The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labeled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple currents of A2 and D4, respectively.