Supersymmetric WZW models and twisted K-theory of SO(3)

TL;DR

This paper investigates D-brane charges in supersymmetric SO(3) WZW models, calculating twisted K-theories and confirming their consistency with conformal field theory results, thus advancing understanding of supersymmetric models on non-simply connected groups.

Contribution

It provides a comprehensive analysis of D-brane charges in supersymmetric SO(3) WZW models, including novel twisted models and their K-theoretic classification.

Findings

Twisted K-theories match CFT D-brane charge calculations.

Identifies two distinct supersymmetric CFTs at each even level.

Clarifies aspects of N=1 supersymmetric WZW models on non-simply connected groups.

Abstract

We present an encompassing treatment of D-brane charges in supersymmetric SO(3) WZW models. There are two distinct supersymmetric CFTs at each even level: the standard bosonic SO(3) modular invariant tensored with free fermions, as well as a novel twisted model. We calculate the relevant twisted K-theories and find complete agreement with the CFT analysis of D-brane charges. The K-theoretical computation in particular elucidates some important aspects of N=1 supersymmetric WZW models on non-simply connected Lie groups.