Max Hubner, David R. Morrison, Sakura SchÃ¤ferNameki, YiNan Wang
SciPost Phys. 13, 030 (2022) ·
published 19 August 2022

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We realize higherform symmetries in Ftheory compactifications on
noncompact elliptically fibered CalabiYau manifolds. Central to this
endeavour is the topology of the boundary of the noncompact elliptic
fibration, as well as the explicit construction of relative 2cycles in terms
of Lefschetz thimbles. We apply the analysis to a variety of elliptic
fibrations, including geometries where the discriminant of the elliptic
fibration intersects the boundary. We provide a concrete realization of the
1form symmetry group by constructing the associated charged line operator from
the elliptic fibration. As an application we compute the symmetry topological
field theories in the case of elliptic threefolds, which correspond to mixed
anomalies in 5d and 6d theories.
SciPost Phys. 12, 127 (2022) ·
published 12 April 2022

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We study the orbifold singularities $X=\mathbb{C}^3/\Gamma$ where $\Gamma$ is a finite subgroup of $SU(3)$. Mtheory on this orbifold singularity gives rise to a 5d SCFT, which is investigated with two methods. The first approach is via 3d McKay correspondence which relates the group theoretic data of $\Gamma$ to the physical properties of the 5d SCFT. In particular, the 1form symmetry of the 5d SCFT is read off from the McKay quiver of $\Gamma$ in an elegant way. The second method is to explicitly resolve the singularity $X$ and study the Coulomb branch information of the 5d SCFT, which is applied to toric, nontoric hypersurface and complete intersection cases. Many new theories are constructed, either with or without an IR quiver gauge theory description. We find that many resolved CalabiYau threefolds, $\widetilde{X}$, contain compact exceptional divisors that are singular by themselves. Moreover, for certain cases of $\Gamma$, the orbifold singularity $\mathbb{C}^3/\Gamma$ can be embedded in an elliptic model and gives rise to a 6d (1,0) SCFT in the Ftheory construction. Such 6d theory is naturally related to the 5d SCFT defined on the same singularity. We find examples of rank1 6d SCFTs without a gauge group, which are potentially different from the rank1 Estring theory.