Fibrewise T-Duality for D-Branes on Elliptic Calabi-Yau

TL;DR

This paper explores fibrewise T-duality for D-branes on elliptic Calabi-Yau manifolds, revealing the necessity of twisting charges and connecting the duality to known monodromies within mirror symmetry.

Contribution

It demonstrates that fibrewise T-duality requires a natural twisting of charges and relates this duality to monodromies in mirror symmetry.

Findings

Fibrewise T-duality involves a natural twisting of D-brane charges.

The duality is expressed through known monodromies in mirror symmetry.

Twisted charges are essential for the proper application of T-duality.

Abstract

Fibrewise T-duality (Fourier-Mukai transform) for D-branes on an elliptic Calabi-Yau $X$ is shown to require naturally an appropriate twisting of the operation respectively a twisted charge. The fibrewise T-duality is furthermore expressed through known monodromies in the context of Kontsevich's interpretation of mirror symmetry.