Sara Pasquetti, Shlomo S. Razamat, Matteo Sacchi, Gabi Zafrir
SciPost Phys. 8, 014 (2020) ·
published 29 January 2020
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We discuss compactifications of rank $Q$ E-string theory on a torus with
fluxes for abelian subgroups of the $E_8$ global symmetry of the $6d$ SCFT. We
argue that the theories corresponding to such tori are built from a simple
model we denote as $E[USp(2Q)]$. This model has a variety of non trivial
properties. In particular the global symmetry is $USp(2Q)\times USp(2Q)\times
U(1)^2$ with one of the two $USp(2Q)$ symmetries emerging in the IR as an
enhancement of an $SU(2)^Q$ symmetry of the UV Lagrangian. The $E[USp(2Q)]$
model after dimensional reduction to $3d$ and a subsequent Coulomb branch flow
is closely related to the familiar $3d$ $T[SU(Q)]$ theory, the model residing
on an S-duality domain wall of $4d$ $\mathcal{N}=4$ $SU(Q)$ SYM. Gluing the
$E[USp(2Q)]$ models by gauging the $USp(2Q)$ symmetries with proper admixtures
of chiral superfields gives rise to systematic constructions of many examples
of $4d$ theories with emergent IR symmetries. We support our claims by various
checks involving computations of anomalies and supersymmetric partition
functions. Many of the needed identities satisfied by the supersymmetric
indices follow directly from recent mathematical results obtained by E. Rains.
