| Summary: | 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.
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