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Coulomb and Higgs Branches from Canonical Singularities: Part 0
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abstract
Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities. We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d $\mathcal{N}=4$ mirror symmetry and an $S$-type gauging of an abelian flavor symmetry. In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers from the geometry. As an application of the general framework, we observe that singularities that engineer Argyres-Douglas theories in Type IIB also give rise to rank-0 5d SCFTs in M-theory. We also compute the higher-form symmetries of the 4d and 5d SCFTs, including the one-form symmetries of generalized Argyres-Douglas theories of type $(G, G')$.
Forward citations
Cited by 6 Pith papers
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5d Higgs Branches: Stratifications from Geometry
Dynamical complex structure deformations of non-compact Calabi-Yau threefolds with non-isolated singularities reproduce the full Higgs branch stratification of 5d SCFTs, matching magnetic quiver predictions.
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Remarks on the Higgs Branch of 5d Conformal Matter
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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(-1)-form symmetries from M-theory and SymTFTs
A systematic M-theory construction of SymTFTs for discrete and continuous (-1)-form symmetries, with a new 4-group structure in 4d N=1 SYM from G2 manifolds.
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A Bound on 3d Mirror Pairs
New 3d mirror pairs are proposed for ABCD-type quivers with mixed U/SU nodes, and it is conjectured that unitary quivers containing exceptional affine Dynkin subquivers have no Lagrangian quiver mirror.
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An exceptionally simple family of Orthosymplectic 3d $\mathcal{N}=4$ rank-0 SCFTs
A new family of 3d N=4 orthosymplectic quiver theories has trivial Higgs branches and non-trivial Coulomb branches; the smallest full moduli space is two copies of the one-F4 instanton moduli space.
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A Crash Course in Supersymmetric Field Theory Across Dimensions
Pedagogical crash-course notes on supersymmetric field theory across 2–10 dimensions, organized around recurring structures such as holomorphy, dualities, indices, BPS data, and anomalies.
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