Extended affine Lie algebras, vertex algebras and equivariant φ-coordinated quasi-modules

For any nullity 2 extended affine Lie algebra epsilon of maximal type and l is an element of C, we prove that there exist a vertex algebra V-epsilon(l) and an automorphism group G of V-epsilon(l) equipped with a linear character chi, such that the category of restricted epsilon-modules of level l is canonically isomorphic to the category of (G, chi)-equivariant phi-coordinated quasi V epsilon(l)-modules. Moreover, when l is a nonnegative integer, there is a quotient vertex algebra L-epsilon(l) of V-epsilon(l) modulo by a G-stable ideal, and we prove that the integrable restricted epsilon-modules of level l are exactly the (G, chi)-equivariant phi-coordinated quasi-L-epsilon(l)-modules.