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<p>In this work we consider the relation between finite isometries of the internal space and symmetries of the transverse field theory in Geometric Engineering. On top of the established relation between branes wrapping torsional cycles and topological defects, we study other symmetries of the field theory that are not captured by branes wrapped at infinity. Isometries of the engineering geometry have a representations on the field theory, encoded by their non-trivial actions on exceptional and torsional cycles. In this work we describe such action in general terms. As examples, we focus on three classes of geometric engineering spaces: Du Val singularities, toric Calabi-Yau threefolds and <i>G</i><sub>2</sub> manifolds obtained as fibrations of Du Val singularities over <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26941_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi mathvariant="double-struck">S</mi> <mn>3</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {\mathbbm{S}}^3 \)</EquationSource> </InlineEquation>. In the latter case, we check explicitly that M-theory on Calabi-Yau or <i>G</i><sub>2</sub> manifold with finite isometries reproduces correctly the higher group structures and non-invertible symmetries of the transverse field theories.</p>

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Symmetries beyond branes: geometric engineering and isometries

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月12日

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  • Mario De Marco,
  • Shani Nadir Meynet

摘要

In this work we consider the relation between finite isometries of the internal space and symmetries of the transverse field theory in Geometric Engineering. On top of the established relation between branes wrapping torsional cycles and topological defects, we study other symmetries of the field theory that are not captured by branes wrapped at infinity. Isometries of the engineering geometry have a representations on the field theory, encoded by their non-trivial actions on exceptional and torsional cycles. In this work we describe such action in general terms. As examples, we focus on three classes of geometric engineering spaces: Du Val singularities, toric Calabi-Yau threefolds and G2 manifolds obtained as fibrations of Du Val singularities over S 3 \( {\mathbbm{S}}^3 \) . In the latter case, we check explicitly that M-theory on Calabi-Yau or G2 manifold with finite isometries reproduces correctly the higher group structures and non-invertible symmetries of the transverse field theories.