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Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons | Ling Bao
; Axel Kleinschmidt
; Bengt E. W. Nilsson
; Daniel Persson
; Boris Pioline
; | Date: |
26 May 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 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]. | Source: | arXiv, 1005.4848 | Services: | Forum | Review | PDF | Favorites |
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