A symplectic covariant formulation of special Kahler geometry in superconformal calculus

TL;DR

This paper introduces a symplectic covariant formulation of special Kahler geometry within superconformal calculus, enabling vector multiplet couplings in N=2 supergravity without relying on a prepotential.

Contribution

It develops a novel symplectic covariant framework for special Kahler geometry that extends previous definitions and does not depend on a prepotential, using superconformal tensor calculus.

Findings

Provides a symplectic covariant formulation of vector multiplet couplings.

Extends the definition of special Kahler manifolds beyond traditional constraints.

Enables on-shell vector multiplets through a superconformal approach.

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.