The Geometry of the SU(2)$\times$ G${}_2$-model

Abstract

We study elliptic fibrations that geometrically engineer an SU(2)$\times$ G${}_2$ gauge theory realized by Weierstrass model for the collision III+${\text{I}}_0^{\ast \text{ns}}$. We construct the four possible crepant resolutions of such a Weierstrass model and show that they form a chain of four minimal models connected by flops. We compute the generating function for the Euler characteristic of these crepant resolutions. In the case of a Calabi-Yau threefold, we consider the compactification of M-theory and F-theory on an SU(2)$\times$ G${}_2$-model to a five and six-dimensional supergravity with eight supercharges. By matching each crepant resolution with each Coulomb chamber of the five-dimensional theory, we determine the number of multiplets and compute the prepotential in each Coulomb chamber. In particular, we discuss counting number of hypermultiplets in presence of singularities. We discuss in detail the cancellation of anomalies of the six-dimensional theory.

43 pages + references, 14 tables, 11 figures

References in corpus (10)

• 6d Conformal Matter
• On Geometric Classification of 5d SCFTs
• D-brane Deconstructions in IIB Orientifolds
• Global aspects of the space of 6D N = 1 supergravities
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Quantization of anomaly coefficients in 6D $\mathcal{N}=(1,0)$ supergravity
• 6d SCFTs and U(1) Flavour Symmetries
• 4D Gauge Theories with Conformal Matter
• Exotic matter on singular divisors in F-theory
• Geometric engineering on flops of length two

Cited by in corpus (18)

• Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
• Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank
• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
• Trifectas for $T_N$ in 5d
• Twisted Circle Compactifications of 6d SCFTs
• Classification of 5d N=1 gauge theories
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• 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
• Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Infinitely many 4d N=1 SCFTs with a=c
• Fibre-base duality of 5d KK theories
• Magic square and half-hypermultiplets in F-theory
• Isomorphisms of 4d N=2 SCFTs from 6d
• Non-split singularities and conifold transitions in F-theory