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<p>We show that scale-invariant special Kähler geometries whose generic <i>r</i> dim<sub><i>ℂ</i></sub> abelian variety fiber is isomorphic (completely split) or isogenous (completely iso-split) as a complex torus to the product of <i>r</i> one-dimensional complex tori have constant <i>τ</i><sup><i>ij</i></sup> modulus on the Coulomb branch, i.e. are isotrivial. These simple results are useful in organizing the classification of scale-invariant special Kähler geometries, which, in turn, is relevant to the classification of possible 4-dimensional <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26411_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 2 supersymmetric superconformal field theories.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月11日

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  • Philip C. Argyres,
  • Robert Moscrop,
  • Souradeep Thakur,
  • Mitch Weaver

摘要

We show that scale-invariant special Kähler geometries whose generic r dimℂ 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 τij modulus on the Coulomb branch, i.e. are isotrivial. These simple results are useful in organizing the classification of scale-invariant special Kähler geometries, which, in turn, is relevant to the classification of possible 4-dimensional N \( \mathcal{N} \) = 2 supersymmetric superconformal field theories.