Four dimensional superconformal theories from M5 branes

We study N=1 superconformal theories in four dimensions obtained wrapping M5 branes on a Riemann surface. We propose a method to determine from the spectral curve the scaling dimension of chiral operators in the SCFT. Whenever the R-symmetry has to be determined via a-maximization, our procedure allows us to determine the charge of chiral operators under the “trial” R-symmetry. Our proposal reduces to the correct prescription in the special case of N=2 theories of class S . We perform several consistency checks and apply our method to study some new SCFT’s such as N=1 deformations of Argyres-Douglas theories.