Quarter BPS operators in Script N = 4 SYM

Chiral primary operators annihilated by a quarter of the supercharges areconstructed in the four dimensional N=4 Super-Yang-Mills theory with gaugegroup SU(N). These quarter-BPS operators share many non-renormalizationproperties with the previously studied half-BPS operators. However, they aremuch more involved, which renders their construction nontrivial in the fullyinteracting theory. In this paper we calculate order g^2 two-point functions oflocal, polynomial, scalar composite operators within a given representation ofthe SU(4) R-symmetry group. By studying these two-point functions, we identifythe eigenstates of the dilatation operator, which turn out to be complicatedmixtures of single and multiple trace operators. Given the elaborate combinatorics of this problem, we concentrate on twospecial cases. First, we present explicit computations for quarter-BPSoperators with scaling dimension Delta < 8. In this case, the discussionapplies to arbitrary N of the gauge group. Second, we carry out a leading plussubleading large N analysis for the particular class of operators built out ofdouble and single trace operators only. The large N construction addressesquarter-BPS operators of general dimension.Comment: 38 pages, Latex, eps figures, uses epsfig.sty; references adde