Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons

6th International Symposium on Quantum Theory and Symmetries

Bao, L.^1 ; Kleinschmidt, A.^2 ; Nilsson, B.E.W.^3 ; Persson, D.^4 ; Pioline, B.^5

Institut des Hautes Etudes Scientifiques, Le Bois-Marie 35, 91440 Bures-sur-Yvette, France^1

Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine CP 231, Boulevard du Triomphe, 1050 Brussels, Belgium^2

Fundamental Physics, Chalmers University of Technology, SE-412 96, Göteborg, Sweden^3

Institut für Theoretische Physik, Eidgenössische Technische Hochschule, CH-8093 Zürich, Switzerland^4

Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, Université Pierre et Marie Curie-Paris 6, 4 place Jussieu, 75252 Paris Cedex 05, France^5

关键词: Complex multiplication;    Fourier expansion;    Gaussian integers;    Instantons;    Modular group;    Moduli space;    Non-perturbative effects;    Quantum correction;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/462/1/012026/pdf
DOI  :  10.1088/1742-6596/462/1/012026

来源: IOP

【 摘 要 】

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= [i].