HYPERGRAV · The last piece of the puzzle: Off-shell hypermultiplets in string theory and complex geometry

The hypermultiplet sector in N=2 supersymmetric theories has long defied a complete understanding. However, recent workon the couplings of off-shell hypermultiplets in flat space has opened the door to a comprehensive treatment of their supergravity couplings. In pursuit of this goal, this proposal aims to construct a complete description of off-shell N=2 supergravity-matter actions, including both vector and hypermultiplets. This will (i) shed light on the moduli spaces of low energy effective actions of string theory; (ii) enable computations of hypermultiplet contributions to the thermodynamic properties of supersymmetric black holes; and (iii) allow the efficient application of localization to both the hypermultiplet and vector multiplet sectors. The success of this project will place our understanding of N=2 supersymmetric systems on a firm foundation, while at the same time giving new cross-disciplinary insight into the fields of complex geometry and quantum gravity.