An illustrated guide to D-branes in SU(3)

TL;DR

This paper provides a comprehensive classification of symmetric D-branes in the Lie group SU(3), linking their classical and quantum moduli spaces to affine Lie algebra representations and twisted K-theory.

Contribution

It systematically characterizes the moduli spaces of (twisted) conjugacy classes and relates D-brane charges to twisted K-theory, offering a detailed mathematical framework.

Findings

Classified classical and quantum moduli spaces of D-branes in SU(3)

Established correspondence between conjugacy classes and affine Lie algebra representations

Connected D-brane charges to twisted K-theory groups

Abstract

We give a systematic account of symmetric D-branes in the Lie group SU(3). We determine both the classical and quantum moduli space of (twisted) conjugacy classes in terms of the (twisted) Stiefel diagram of the Lie group. We show that the allowed (twisted) conjugacy classes are in one-to-one correspondence with the integrable highest weight representations of the (twisted) affine Lie algebra. In particular, we show how the charges of these D-branes fit in the twisted K-theory groups.