ON CONFORMAL FIELD-THEORIES IN 4 DIMENSIONS

Extending recent work of Kachru and Silverstein, we consider ''orbifol ds'' of four-dimensional N = 4 SU(n) super-Yang-Mills theories with re spect to discrete subgroups of the SU(4) R-symmetry which act non-triv ially on the gauge group. We show that for every discrete subgroup of SU(4) there is a canonical choice of imbedding of the discrete group i n the gauge group which leads to theories with a vanishing one-loop be ta-function. We conjecture that these give rise to (generically non-su persymmetric) conformal theories. The gauge group is x(i)SU(Nn(i)), wh ere n(i) denote the dimension of the irreducible representations of th e corresponding discrete group; there is also bifundamental matter, di ctated by associated quiver diagrams. The interactions can also be rea d off from the quiver diagram. For SU(3) and SU(2) subgroups this lead s to superconformal theories with N = 1 and N = 2, respectively. In th e N = 1 case we prove the vanishing of the beta functions to two loops . (C) 1998 Elsevier Science B.V.