Non-perturbative effects in the BMN limit of Script N=4 supersymmetric Yang-Mills

Abstract

One-instanton contributions to the correlation functions of two gauge-invariant single-trace operators in Yang-Mills theory are studied in semi-classical approximation in the BMN limit. The most straightforward examples involve operators with four bosonic impurities (whereas examples with two-impurity operators pose technical problems). The explicit form for the correlation functions, which determine the anomalous dimensions, follows after integration over the large number of bosonic and fermionic moduli. Our results demonstrate that the instanton contributions scale appropriately in the BMN limit. We find impressive agreement with the D-instanton contributions to mass matrix elements of the dual plane-wave IIB superstring theory, obtained in a previous paper. Not only does the dependence on the scaled coupling constants match, but the dependence on the mode numbers of the states is also in striking agreement.