Comments on D-branes on Orbifolds and K-theory

TL;DR

This paper revisits the classification of D-branes on orbifolds using K-theory, confirming minimal charge predictions and aligning K-theory with boundary state methods for various orbifold types.

Contribution

It provides a detailed comparison between K-theory classification and boundary state formalism for D-branes on orbifolds, including cases with discrete torsion.

Findings

Minimally charged branes in Z_N orbifolds with odd N are BPS.

K-theory classification matches boundary state results for Z_N x Z_N orbifolds.

Boundary state formalism confirms the types of Chan-Paton representations predicted by K-theory.

Abstract

We systematically revisit the description of $D$-branes on orbifolds and the classification of their charges via K-theory. We include enough details to make the results accessible to both physicists and mathematicians interested in these topics. The minimally charged branes predicted by K-theory in Z_N orbifolds with $N$ odd are only BPS. We confirm this result using the boundary state formalism for Z_3. For Z_N x Z_N orbifolds with and without discrete torsion, we show that the K-theory classification of charges agrees with the boundary state approach, largely developed by Gaberdiel and collaborators, including the types of representation on the Chan-Paton factors.