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arXiv · 2410.22027

T-dual branes on hyperk\"ahler manifolds

Maria Anna Sisak
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Abstract

This submission is a PhD dissertation. Kapustin and Witten conjectured that there is a mirror symmetry relation between the hyperk\"ahler 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 hyperk\"ahler structures on algebraic integrable systems. In this thesis, we investigate the T-duality relation between hyperk\"ahler structures and the corresponding branes on affine torus bundles. We use the techniques of generalized geometry to show that semi-flat hyperk\"ahler 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.

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Maria Anna Sisak. 2024-10-29. T-dual branes on hyperk\"ahler manifolds. https://doi.org/10.15479/at%3Aista%3A18443

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