BMN operators and string field theory

TL;DR

This paper compares gauge theory calculations of the SYM dilatation operator with string field theory predictions in the pp-wave background, finding a discrepancy that can be resolved with modified matrix elements.

Contribution

It identifies a discrepancy between gauge theory and string field theory results and proposes a modification to reconcile the two at higher orders.

Findings

Modified matrix elements reproduce anomalous dimensions accurately.

Discrepancy with standard SFT results is resolved by the proposed modification.

No contact interaction needed in the single string sector after modification.

Abstract

We extract from gauge theoretical calculations the matrix elements of the SYM dilatation operator. By the BMN correspondence this should coincide with the 3-string vertex of light cone string field theory in the pp-wave background. We find a mild but important discrepancy with the SFT results. If the modified $O(g_2)$ matrix elements are used, the $O(g_2^2)$ anomalous dimensions are exactly reproduced without the need for a contact interaction in the single string sector.