Quarter BPS Operators in N=4 SYM

TL;DR

This paper constructs and analyzes quarter-BPS operators in N=4 SYM, calculating their two-point functions at order g^2, identifying eigenstates of the dilatation operator, and exploring their structure for various dimensions and large N limits.

Contribution

It provides the first detailed construction and two-point function analysis of quarter-BPS operators in N=4 SYM, including explicit results for low dimensions and large N behavior.

Findings

Eigenstates of the dilatation operator are complex mixtures of single and multiple traces.

Explicit two-point functions computed for operators with dimension less than 8.

Large N analysis of quarter-BPS operators built from single and double traces.

Abstract

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 quarter-BPS operators share many non-renormalization properties with the previously studied half-BPS operators. However, they are much more involved, which renders their construction nontrivial in the fully interacting theory. In this paper we calculate order 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 quarter-BPS operators with scaling dimension Delta < 8. 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 quarter-BPS operators of general dimension.