BMN operators and string field theory

TL;DR

The paper tests the BMN gauge/string duality by extracting the order $O(g_2)$ dilatation-operator matrix elements from gauge theory and identifying them with the $O(g_s)$ light-cone string field theory vertex in the pp-wave background. It shows that these gauge-theory elements, when combined with a modified SFT vertex, correctly reproduce the $O(g_2^2)$ anomalous dimensions without invoking contact terms in the single-string sector, even though there is a mild mismatch with the standard SV1 vertex and partial agreement with SV2. This provides support for a string-field-theory interpretation while highlighting subtle asymmetries and the need to reconcile the vertex with continuum SFT formulations. The work also points toward future exploration of discrete string-bit descriptions and the precise mapping between gauge-theory data and string-field-theory constructs in the pp-wave regime.

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.