Max Hubner, David R. Morrison, Sakura Schäfer-Nameki, Yi-Nan Wang
SciPost Phys. 13, 030 (2022) ·
published 19 August 2022
|
· pdf
We realize higher-form symmetries in F-theory compactifications on
non-compact elliptically fibered Calabi-Yau manifolds. Central to this
endeavour is the topology of the boundary of the non-compact elliptic
fibration, as well as the explicit construction of relative 2-cycles 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
1-form 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 three-folds, which correspond to mixed
anomalies in 5d and 6d theories.
SciPost Phys. 12, 127 (2022) ·
published 12 April 2022
|
· pdf
We study the orbifold singularities $X=\mathbb{C}^3/\Gamma$ where $\Gamma$ is a finite subgroup of $SU(3)$. M-theory 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 1-form 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, non-toric 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 Calabi-Yau 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 F-theory construction. Such 6d theory is naturally related to the 5d SCFT defined on the same singularity. We find examples of rank-1 6d SCFTs without a gauge group, which are potentially different from the rank-1 E-string theory.
