Completely (iso-)split scale-invariant Coulomb branch geometries are isotrivial
arxiv(2024)
摘要
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 τ^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.
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