2010/05/26 by Ling Bao, Axel Kleinschmidt, Bao, Ling +7 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1005.4848
openalex publication_date 2010/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Od, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2,1;Od). 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 O1=Z[i].