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The symplectic structure of \(N=2\) supergravity and its central extension. (English) Zbl 0957.81691

Summary: We report on the formulation of \(N=2, D=4\) supergravity coupled to \(n_V\) abelian vector multiplets in presence of electric and magnetic charges. General formulae for the (moduli dependent) electric and magnetic charges for the \(n_V + 1\) gauge fields are given which reflect the symplectic structure of the underlying special geometry. Model independent sum rules obeyed by these charges are obtained. The specification to Type IIB strings compactified on Calabi-Yau manifolds, with gauge group U\((1)^h21^{+1}\), is given.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
32J81 Applications of compact analytic spaces to the sciences
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
83E50 Supergravity
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