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• W3099366013 abstract "We study D-branes wrapping an exceptional four-cycle P(1,a,b) in a blown-up C 3 /Z m non-compact Calabi–Yau threefold with (m;a,b)=(3;1,1), (4;1,2) and (6; 2, 3). In applying the method of local mirror symmetry we find that the Picard–Fuchs equations for the local mirror periods in the Z 3,4,6 orbifolds take the same form as the ones in the local E 6,7,8 del Pezzo models, respectively. It is observed, however, that the orbifold models and the del Pezzo models possess different physical properties because the background NS B-field is turned on in the case of Z 3,4,6 orbifolds. This is shown by analyzing the periods and their monodromies in full detail with the help of Meijer G-functions. We use the results to discuss D-brane configurations on P(1,a,b) as well as on del Pezzo surfaces. We also discuss the number theoretic aspect of local mirror symmetry and observe that the exponent which governs the exponential growth of the Gromov–Witten invariants is determined by the special value of the Dirichlet L-function." @default.
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• W3099366013 date "2001-06-01" @default.
• W3099366013 modified "2023-09-23" @default.
• W3099366013 title "CLOSED SUB-MONODROMY PROBLEMS, LOCAL MIRROR SYMMETRY AND BRANES ON ORBIFOLDS" @default.
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• W3099366013 doi "https://doi.org/10.1142/s0129055x01000867" @default.
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