A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models

TL;DR

This paper proves that algebraic and geometric definitions of D-brane charges in WZW models are equivalent for all simple Lie groups, and calculates the charge group based on geometric ambiguities.

Contribution

It establishes the equality of algebraic and geometric D-brane charges and computes the charge group from geometric ambiguities in WZW models.

Findings

Algebraic and geometric charges coincide for all simple Lie groups.

The charge group is explicitly computed from geometric ambiguities.

Provides a unified understanding of D-brane charge definitions in WZW models.

Abstract

The algebraic definition of charges for symmetry-preserving D-branes in Wess-Zumino-Witten models is shown to coincide with the geometric definition, for all simple Lie groups. The charge group for such branes is computed from the ambiguities inherent in the geometric definition.