T-dual branes on hyperkähler manifolds ISTA Thesis Sisak, Maria A hyperkaehler geometry branes mirror symmetry T-duality ddc:516 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. Institute of Science and Technology Austria 2024 info:eu-repo/semantics/doctoralThesis doc-type:doctoralThesis text http://purl.org/coar/resource_type/c_db06 https://research-explorer.ista.ac.at/record/18443 https://research-explorer.ista.ac.at/download/18443/18467 Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:<a href="https://doi.org/10.15479/at:ista:18443">10.15479/at:ista:18443</a> eng info:eu-repo/semantics/altIdentifier/doi/10.15479/at:ista:18443 info:eu-repo/semantics/altIdentifier/issn/2663-337X https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess