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A symplectic covariant formulation of special Kahler geometry in superconformal calculus

Piet Claus·Kor Van Hoof·Antoine Van Proeyen
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Abstract

We present a formulation of the coupling of vector multiplets to N=2 supergravity which is symplectic covariant (and thus is not based on a prepotential) and uses superconformal tensor calculus. We do not start from an action, but from the combination of the generalised Bianchi identities of the vector multiplets in superspace, a symplectic definition of special Kahler geometry, and the supersymmetric partners of the corresponding constraints. These involve the breaking to super-Poincare symmetry, and lead to on-shell vector multiplets. This symplectic approach gives the framework to formulate vector multiplet couplings using a weaker defining constraint for special Kahler geometry, which is an extension of older definitions of special Kahler manifolds for some cases with only one vector multiplet.

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Piet Claus, Kor Van Hoof, Antoine Van Proeyen. 1999-06-15. A symplectic covariant formulation of special Kahler geometry in superconformal calculus. https://doi.org/10.1088/0264-9381%2F16%2F8%2F305

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