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.
Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Superconformal five dimensional theories have a rich structure of phases and brane webs play a crucial role in studying their properties. This paper is devoted to the study of a three parameter family of SQCD theories, given by the number of colors $N_c$ for an $SU(N_c)$ gauge theory, number of fundamental flavors $N_f$, and the Chern Simons level $k$. The study of their infinite coupling Higgs branch is a long standing problem and reveals a rich pattern of moduli spaces, depending on the 3 values in a critical way. For a generic choice of the parameters we find a surprising number of 3 different components, with intersections that are closures of height 2 nilpotent orbits of the flavor symmetry. This is in contrast to previous studies where except for one case ($N_c=2, N_f=2$), the parameters were restricted to the cases of Higgs branches that have only one component. The new feature is achieved thanks to a concept in tropical geometry which is called stable intersection and allows for a computation of the Higgs branch to almost all the cases which were previously unknown for this three parameter family apart form certain small number of exceptional theories with low rank gauge group. A crucial feature in the construction of the Higgs branch is the notion of dressed monopole operators.
fields
hep-th 4representative citing papers
Blow-up equation prefactors encode cubic 1-form self-anomalies and mixed anomalies of 5d N=1 SCFTs, deciding 2-group vs mixed anomaly structure.
A 3D N=4 gauge theory is built via U(1) gauging whose Higgs branch matches a known symplectic singularity, with a proposed non-simply laced magnetic quiver mirror validated through standard 3D mirror symmetry tests.
Proposes conjectural central charge formulas for 2d N=(0,4) theories from class S reductions and verifies agreement via Hilbert series on special and twisted Higgs branches for SU(2) cases.
citing papers explorer
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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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Generalised global symmetries in 5d $\mathcal{N}=1$ theories from the blow-up equations
Blow-up equation prefactors encode cubic 1-form self-anomalies and mixed anomalies of 5d N=1 SCFTs, deciding 2-group vs mixed anomaly structure.
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A Tale of Two Orbits: Non-Simply Laced Mirror
A 3D N=4 gauge theory is built via U(1) gauging whose Higgs branch matches a known symplectic singularity, with a proposed non-simply laced magnetic quiver mirror validated through standard 3D mirror symmetry tests.
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Central Charges and Vacuum Moduli of 2d $\mathcal{N}=(0,4)$ Theories from Class $\mathcal{S}$
Proposes conjectural central charge formulas for 2d N=(0,4) theories from class S reductions and verifies agreement via Hilbert series on special and twisted Higgs branches for SU(2) cases.