Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons
Paper in proceedings, 2010

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 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].

rigid calabi-yau

number theory

String theory


Bengt E W Nilsson

Chalmers, Applied Physics, Mathematical Physics

Axel Kleinschmidt

Daniel Persson

Boris Pioline

roceedings of 6th International Symposium on Quantum Theory and Symmetries (QTS6), Lexington, Kentucky, 20-25 Jul 2009.

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