Geometric engineering on flops of length two

Abstract

Type IIA on the conifold is a prototype example for engineering QED with one charged hypermultiplet. The geometry admits a flop of length one. In this paper, we study the next generation of geometric engineering on singular geometries, namely flops of length two such as Laufer's example, which we affectionately think of as the $conifold2.0$. Type IIA on the latter geometry gives QED with higher-charge states. In type IIB, even a single D3-probe gives rise to a nonabelian quiver gauge theory. We study this class of geometries explicitly by leveraging their quiver description, showing how to parametrize the exceptional curve, how to see the flop transition, and how to find the noncompact divisors intersecting the curve. With a view towards F-theory applications, we show how these divisors contribute to the enhancement of the Mordell-Weil group of the local elliptic fibration defined by Laufer's example.

41 pages, 6 figures, 1 appendix; v2: typos fixed, version published in JHEP

References in corpus (2)

• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• E3-brane instantons and baryonic operators for D3-branes on toric singularities

Cited by in corpus (12)

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• The Geometry of the SU(2)$\times$ G${}_2$-model
• F-Theory on Quotients of Elliptic Calabi-Yau Threefolds
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• Genus zero Gopakumar-Vafa invariants from open strings
• High electric charges in M-theory from quiver varieties
• 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
• An infinite swampland of U(1) charge spectra in 6D supergravity theories
• Geometric Unification of Higgs Bundle Vacua
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs