Summary: We consider M-theory on \((T^2\times \mathbb{R}^2)/\mathbb{Z}_n\) with M5-branes wrapped on \(\mathbb{R}^2\). One can probe this background with M5-branes wrapped on \(T^2\). The theories on the probes provide many new examples of \(N=2\) field theories without Lagrangian description. All these theories have Coulomb branches, and we find the corresponding Seiberg-Witten curves. The exact solution is encoded in a Hitchin system on an orbifolded torus with punctures. The theories we consider also arise from D3 probes in F-theory on \(K3\times K3\) orbifolds. Interestingly, the relevant F-theory background has frozen \(\mathbb{Z}_n\) singularities which are analogous to frozen \(\mathbb{Z}_2\) singularities in type I string theory. We use the F-theory description to find supergravity duals of the probe SCFT’s in the large-\(N\) limit and compute the spectrum of relevant and marginal operators. We also explain how the decoupling of U(1) factors is manifested in the supergravity description.

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