@phdthesis{18443,
abstract = {In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between
the hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they
conjecture an equivalence between categories of BBB and BAA-branes. At the classical
level, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on
algebraic integrable systems.
In this thesis, we investigate the T-duality relation between hyperkähler structures and the
corresponding branes on affine torus bundles. We use the techniques of generalized geometry
to show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.
We also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform
we upgrade the T-duality between generalized branes to T-duality of submanifolds endowed
with U(1)-bundles and connections. This T-duality in the appropriate context specializes to
T-duality between BBB and BAA-branes.
},
author = {Sisak, Maria A},
issn = {2663-337X},
keywords = {hyperkaehler geometry, branes, mirror symmetry, T-duality},
pages = {178},
publisher = {Institute of Science and Technology Austria},
title = {{T-dual branes on hyperkähler manifolds}},
doi = {10.15479/at:ista:18443},
year = {2024},
}