  In this paper we study compactifications of ADE type conformal matter, N M5
branes probing ADE singularity, on torus with flux for global symmetry. We
systematically construct the four dimensional theories by first going to five
dimensions and studying interfaces. We claim that certain interfaces can be
associated with turning on flux in six dimensions. The interface models when
compactified on a circle comprise building blocks for constructing four
dimensional models associated to flux compactifications of six dimensional
theories on a torus. The theories in four dimensions turn out to be quiver
gauge theories and the construction implies many interesting cases of IR
symmetry enhancements and dualities of such theories.
