T-dual branes on hyperkähler manifolds

By: Material type: TextTextPublication details: Institute of Science and Technology Austria 2024Online resources:
Contents:
Abstract
Acknowledgements
About the Author
Table of Contents
1 Introduction
2 Affine torus bundles and integrable systems
3 Generalized geometry
4 T-duality in generalized geometry
5 Complex tori, Fourier-Mukai transform and factors of automorphy
6 Factors of automorphy on real tori
7 T-duality for U(1)-bundles with connections
8 Conclusions
Bibliography
Summary: 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.
List(s) this item appears in: ISTA Thesis | New Arrivals October 2025
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Thesis

Abstract

Acknowledgements

About the Author

Table of Contents

1 Introduction

2 Affine torus bundles and integrable systems

3 Generalized geometry

4 T-duality in generalized geometry

5 Complex tori, Fourier-Mukai transform and factors of automorphy

6 Factors of automorphy on real tori

7 T-duality for U(1)-bundles with connections

8 Conclusions

Bibliography

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.

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