A geometric interpretation of the c-map.

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.