Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons
Abstract
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].
Keywords
Cite
@article{arxiv.1005.4848,
title = {Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons},
author = {Ling Bao and Axel Kleinschmidt and Bengt E. W. Nilsson and Daniel Persson and Boris Pioline},
journal= {arXiv preprint arXiv:1005.4848},
year = {2010}
}
Comments
8 pages, for the proceedings of Quantum Theories and Symmetries VI