Computing the Scalar Field Couplings in 6D Supergravity

TL;DR

This paper explicitly computes the scalar manifold metric and couplings in 6D supergravity derived from type IIA string theory on K3, and explores geometric correspondences relevant to string compactifications.

Contribution

It provides explicit formulas for scalar field metrics and couplings in 6D supergravity with applications to string compactifications and geometric dualities.

Findings

Derived the scalar manifold metric for 6D supergravity on K3.

Analyzed scalar self-couplings with multiple vector multiplets.

Established a correspondence between hyperKahler and Kahler geometries.

Abstract

Using non chiral supersymmetry in 6D space time, we compute the explicit expression of the metric the scalar manifold $SO(1,1) \times \frac{SO(4,20) }{SO(4) \times SO(20)}$ of the 10D type IIA superstring on generic K3. We consider as well the scalar field self-couplings in the general case where the non chiral 6D supergravity multiplet is coupled to generic n vector supermultiplets with moduli space $SO(1,1) \times \frac{SO(4,n)}{SO(4) \times SO(n)}$. We also work out a dictionary giving a correspondence between hyperKahler geometry and the Kahler geometry of the Coulomb branch of 10D type IIA on Calabi-Yau threefolds. Others features are also discussed.