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Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons

par Bao, Ling;Kleinschmidt, Axel ;Nilsson, Bengt;Persson, Daniel;Pioline, Boris
Référence Journal of physics. Conference series, 462, 1, 012026
Publication Publié, 2013

Article révisé par les pairs

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Résumé :

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 script O signd, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2, 1; script O signd). 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 script O sign1 = ℤ[i].