D-branes, T-duality, and Index Theory

TL;DR

This paper connects D-brane transformations under T-duality with Nahm transforms, extending the mathematical framework to various gauge groups, orbifolds, and identifying the K-theory groups classifying D-brane charges.

Contribution

It generalizes Nahm transform to orthogonal and symplectic gauge groups and orbifolds, and identifies the K-theory isomorphism for D-brane charge classification.

Findings

Nahm transform describes D-brane T-duality on four-torus.

Extended Nahm transform to orthogonal and symplectic gauge groups.

Identified K-theory isomorphism for D-brane charges in various settings.

Abstract

We show that the transformation of D-branes under T-duality on four-torus is represented by Nahm transform of instantons. The argument for this allows us to generalize Nahm transform to the case of orthogonal and symplectic gauge groups as well as to instantons on Z_2 orbifold of four-torus. In addition, we identify the isomorphism of K-theory groups that realizes the transformation of D-brane charges under T-duality on torus of arbitrary dimensions. By the isomorphism we are lead to identify the correct K-theory group that classifies D-brane charges in Type II orientifold.