Michele Del Zotto, Iñaki García Etxebarria, Sakura Schäfer-Nameki
SciPost Phys. 13, 105 (2022) ·
published 8 November 2022
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Quantum Field Theories engineered in M-theory can have 2-group symmetries,
mixing 0-form and 1-form symmetry backgrounds in non-trivial ways. In this
paper we develop methods for determining the 2-group structure from the
boundary geometry of the M-theory background. We illustrate these methods in
the case of 5d theories arising from M-theory on ordinary and generalised toric
Calabi-Yau cones, including cases in which the resulting theory is
non-Lagrangian. Our results confirm and elucidate previous results on 2-groups
from geometric engineering.
SciPost Phys. 6, 052 (2019) ·
published 1 May 2019
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We revisit the correspondence between Calabi-Yau (CY) threefold isolated
singularities $\mathbf{X}$ and five-dimensional superconformal field theories
(SCFTs), which arise at low energy in M-theory on the space-time transverse to
$\mathbf{X}$. Focussing on the case of toric CY singularities, we analyze the
"gauge-theory phases" of the SCFT by exploiting fiberwise M-theory/type IIA
duality. In this setup, the low-energy gauge group simply arises on stacks of
coincident D6-branes wrapping 2-cycles in some ALE space of type $A_{M-1}$
fibered over a real line, and the map between the K\"ahler parameters of
$\mathbf{X}$ and the Coulomb branch parameters of the field theory (masses and
VEVs) can be read off systematically. Different type IIA "reductions" give rise
to different gauge theory phases, whose existence depends on the particular
(partial) resolutions of the isolated singularity $\mathbf{X}$. We also comment
on the case of non-isolated toric singularities. Incidentally, we propose a
slightly modified expression for the Coulomb-branch prepotential of 5d
$\mathcal{N}=1$ gauge theories.
