Completely (iso-)split scale-invariant Coulomb branch geometries are isotrivial

TL;DR

The paper proves that certain scale-invariant special Kahler geometries with completely split or iso-split abelian varieties are isotrivial, meaning their complex structure moduli are constant across the Coulomb branch, aiding classification efforts.

Contribution

It establishes that these geometries have constant moduli, simplifying the classification of scale-invariant special Kahler geometries relevant to N=2 superconformal theories.

Findings

Geometries with completely split or iso-split abelian varieties are isotrivial.

Constant $ au^{ij}$ moduli across the Coulomb branch.

Facilitates classification of N=2 superconformal field theories.

Abstract

We show that scale-invariant special Kahler geometries whose generic r-complex-dimensional abelian variety fiber is isomorphic (completely split) or isogenous (completely iso-split) as a complex torus to the product of r one-dimensional complex tori have constant $\tau^{ij}$ modulus on the Coulomb branch, i.e., are isotrivial. These simple results are useful in organizing the classification of scale-invariant special Kahler geometries, which, in turn, is relevant to the classification of possible 4-dimensional N=2 supersymmetric superconformal field theories.