Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons

L Bao , A Kleinschmidt , B E W Nilsson , D Persson , B Pioline (1, 2, 3)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
2 SU - Sorbonne Université
3 UPMC - Université Pierre et Marie Curie - Paris 6

Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2,1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers O_d, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2,1;O_d). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers O_1=Z[i].

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Théorie des nombres [math.NT]

L Bao, A Kleinschmidt, B E W Nilsson, D Persson, B Pioline. Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons. Journal of Physics: Conference Series, 2013, 462, ⟨10.1088/1742-6596/462/1/012026⟩. ⟨hal-00487420⟩