Quarter BPS operators in N=4 SYM -: art. no. 046

Chiral primary operators annihilated by a quarter of the supercharges are constructed in the four dimensional N = 4 Super-Yang-Mills theory with gauge group SU(N). These 1/4-BPS operators share many non-renormalization properties with the previously studied 1/2-BPS operators. However, they are much more involved, which renders their construction nontrivial in the fully interacting theory. In this paper we calculate O(g(2)) two-point functions of local, polynomial, scalar composite operators within a given representation of the SU(4) R-symmetry group. By studying these two-point functions, we identify the eigenstates of the dilatation operator, which turn out to be complicated mixtures of single and multiple trace operators. Given the elaborate combinatorics of this problem, we concentrate on two special cases. First, we present explicit computations for 1/4-BPS operators with scaling dimension Delta less than or equal to 7. In this case, the discussion applies to arbitrary N of the gauge group. Second, we carry out a leading plus subleading large N analysis for the particular class of operators built out of double and single trace operators only. The large N construction addresses 1/4-BPS operators of general dimension.