Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)

Understand

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.