S-duality in Twistor Space

Sergey Alexandrov (1) , Boris Pioline (2)

1 L2C - Laboratoire Charles Coulomb
2 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Sergey Alexandrov, Boris Pioline. S-duality in Twistor Space. Journal of High Energy Physics, 2012, pp.112. ⟨10.1007/JHEP08(2012)112⟩. ⟨hal-00705850⟩