| dc.description.abstract | T-duality is a duality between type IIA and type IIB superstring theory. After compactification
on a Calabi-Yau3 manifold this duality induces a relation between the vector multiplet moduli
space of type IIB (IIA) and the hypermultiplet moduli space of type IIA (IIB), which is called
the c-map. We have investigated this relation from the geometric point of view of the internal
Calabi-Yau3 manifold, with and without coupling to gravity. In the N = 2 rigid supersymmetry
situation it is known that the c-map constructs a bundle of Griffiths intermediate Jacobians on
the vector multiplet moduli space, while a bundle of Weil intermediate Jacobians is found in the
N = 2 supergravity situation. In the latter case an additional gravitational dilaton-axion system
is connected with the Weil intermediate Jacobians through a dilatationally extended Heisenberg
group structure that amounts from symplectic invariance, dilatational invariance and the Peccei-
Quinn isometries of the Ramond fields and Neveu-Schwarz axion. The total hypermultiplet moduli
space gets therefore the interpretation of a principal-like fibre bundle whose fibres are identified
with a semi-direct product of a subgroup of the symplectic group and a dilatationally extended
Heisenberg group modulo their integer subgroups. The invariant metric on the fibre bundle is given
by a Wess-Zumino-Witten model consisting of the Killing bilinear form acting on the structure
group’s Maurer-Cartan form. | |
