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

TL;DR

This paper investigates non-perturbative instanton effects in N=4 supersymmetric Yang-Mills theory within the BMN limit, revealing results that align with dual string theory predictions for mass matrix elements.

Contribution

It provides explicit calculations of instanton contributions to correlation functions in the BMN limit, demonstrating their scaling and agreement with dual superstring theory results.

Findings

Instanton contributions scale correctly in the BMN limit.

Strong agreement with D-instanton effects in plane-wave string theory.

Dependence on mode numbers matches string theory predictions.

Abstract

One-instanton contributions to the correlation functions of two gauge-invariant single-trace operators in N=4 SU(N) Yang-Mills theory are studied in semi-classical approximation in the BMN limit. The most straightforward examples involve operators with four bosonic impurities. 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.