Flopping and Slicing: SO(4) and Spin(4)-models

Abstract

We study the geometric engineering of gauge theories with gauge group Spin(4) and SO(4) using crepant resolutions of Weierstrass models. The corresponding elliptic fibrations realize a collision of singularities corresponding to two fibers with dual graph the affine $A_1$ Dynkin diagram. There are eight different ways to engineer such collisions using decorated Kodaira fibers. The Mordell-Weil group of the elliptic fibration is required to be trivial for Spin(4) and Z/2Z for SO(4). Each of these models have two possible crepant resolutions connected by a flop. We also compute a generating function for the Euler characteristic of such elliptic fibrations over a base of arbitrary dimensions. In the case of a threefold, we also compute the triple intersection numbers of the fibral divisors. In the case of Calabi-Yau threefolds, we also compute their Hodge numbers, and check the cancellations of anomalies in a six-dimensional supergravity theory.

45 pages+references, 12 figures, and 4 tables

References in corpus (6)

• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• A New Model for Elliptic Fibrations with a Rank One Mordell-Weil Group: I. Singular Fibers and Semi-Stable Degenerations
• T-Branes at the Limits of Geometry
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies
• Singular Geometry and Higgs Bundles in String Theory
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models

Cited by in corpus (10)

• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
• Classification of 5d N=1 gauge theories
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Higgs, Coulomb, and Hall-Littlewood
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models
• Infinitely many 4d N=1 SCFTs with a=c
• Fibre-base duality of 5d KK theories
• Isomorphisms of 4d N=2 SCFTs from 6d