Max Hubner, David R. Morrison, Sakura Schäfer-Nameki, Yi-Nan Wang
SciPost Phys. 13, 030 (2022) ·
published 19 August 2022
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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.
Lakshya Bhardwaj, Max Hubner, Sakura Schafer-Nameki
SciPost Phys. 12, 040 (2022) ·
published 26 January 2022
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We study confinement in 4d N=1 theories obtained by deforming 4d N=2 theories
of Class S. We argue that confinement in a vacuum of the N=1 theory is encoded
in the 1-cycles of the associated N=1 curve. This curve is the spectral cover
associated to a generalized Hitchin system describing the profiles of two Higgs
fields over the Riemann surface upon which the 6d (2,0) theory is compactified.
Using our method, we reproduce the expected properties of confinement in
various classic examples, such as 4d N=1 pure Super-Yang-Mills theory and the
Cachazo-Seiberg-Witten setup. More generally, this work can be viewed as
providing tools for probing confinement in non-Lagrangian N=1 theories, which
we illustrate by constructing an infinite class of non-Lagrangian N=1 theories
that contain confining vacua. The simplest model in this class is an N=1
deformation of the N=2 theory obtained by gauging $SU(3)^3$ flavor symmetry of
the $E_6$ Minahan-Nemeschansky theory.
Dr Hubner: "We thank both referees for the..."
in Submissions | report on Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations