Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions

Cyril Closset; Sakura Schafer-Nameki; Yi-Nan Wang

Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions

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arxiv 2111.13564 v2 pith:SNNEKC2P submitted 2021-11-26 hep-th

Cyril Closset , Sakura Schafer-Nameki , Yi-Nan Wang This is my paper · ORCID

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keywords singularitiescanonicalhypersurfaceisolatedresolutionsscftscalabi-yaucoulomb

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Compactification of M-theory and of IIB string theory on threefold canonical singularities gives rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. The resolutions and deformations of the singularities encode salient features of the SCFTs and of their moduli spaces. In this paper, we build on Part 0 of this series (arXiv:2007.15600) and further explore the physics of SCFTs arising from isolated hypersurface singularities. We study in detail these canonical isolated hypersurface singularities that admit a smooth Calabi-Yau (crepant) resolution. Their 5d and 4d physics is discussed and their 3d reduction and mirrors (the magnetic quivers) are determined in many cases. As an explorative tool, we provide a Mathematica code which computes key quantities for any canonical isolated hypersurface singularity, including the 5d rank, the 4d Coulomb branch spectrum and central charges, higher-form symmetries in 4d and 5d, and crepant resolutions.

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Remarks on the Higgs Branch of 5d Conformal Matter
hep-th 2025-02 conditional novelty 7.0 of 10

The Higgs branches of 5d conformal matter atoms and molecules are computed via magnetic quivers and class-S circle reductions, with matching dimensions across the two methods.

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