D-brane charges on non-simply connected groups

TL;DR

This paper investigates the charges of maximally symmetric D-branes on non-simply connected Lie groups, revealing complex charge group structures influenced by number theoretic properties, with explicit examples for SO(3) and SU(3).

Contribution

It provides a detailed analysis of D-brane charges on non-simply connected groups using conformal field theory, extending understanding beyond simply connected cases.

Findings

Charge groups are generally not cyclic.

Charge equations do not determine charges uniquely.

Explicit charge group structures are derived for specific examples.

Abstract

The maximally symmetric D-branes of string theory on the non-simply connected Lie group SU(n)/Z_d are analysed using conformal field theory methods, and their charges are determined. Unlike the well understood case for simply connected groups, the charge equations do not determine the charges uniquely, and the charge group associated to these D-branes is therefore in general not cyclic. The precise structure of the charge group depends on some number theoretic properties of n, d, and the level of the underlying affine algebra k. The examples of SO(3)=SU(2)/Z_2 and SU(3)/Z_3 are worked out in detail, and the charge groups for SU(n)/Z_d at most levels k are determined explicitly.