High electric charges in M-theory from quiver varieties

Abstract

M-theory on a Calabi-Yau threefold admitting a small resolution gives rise to an Abelian vector multiplet and a charged hypermultiplet. We introduce into this picture a procedure to construct threefolds that naturally host matter with electric charges up to six. These are built as families of Du Val ADE surfaces (or ALE spaces), and the possible charges correspond to the Dynkin labels of the adjoint of the ADE algebra. In the case of charge two, we give a new derivation of the answer originally obtained by Curto and Morrison, and explicitly relate this construction to the Morrison-Park geometry. We also give a procedure for constructing higher-charge cases, which can often be applied to F-theory models.

57 pages, 13 figures, 1 appendix, 1 ancillary Mathematica file (contains very long outputs); v2: minor corrections, version published in JHEP

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• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
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• Charge completeness and the massless charge lattice in F-theory models of supergravity
• Higgs Branches of rank-0 5d theories from M-theory on $(A_j,A_l)$ and $(A_k,D_n)$ singularities
• 5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities
• Holography, Matrix Factorizations and K-stability
• Flops of any length, Gopakumar-Vafa invariants, and 5d Higgs Branches
• Automatic Enhancement in 6D Supergravity and F-theory Models
• Large U(1) charges from flux breaking in 4D F-theory models
• Orders of Vanishing and U(1) Charges in F-theory