Decay widths of three-impurity states in the BMN correspondence

TL;DR

This paper investigates three-impurity states in BMN gauge theory, calculating decay widths and showing agreement with string theory predictions, thus advancing understanding of string-gauge duality at the quantum level.

Contribution

It extends the analysis of BMN gauge theory to three-impurity states at one loop and all genus, providing explicit decay width calculations and matching string theory results.

Findings

Decay widths of three-impurity states are computed.

Single string states are unstable against decay into two-string states.

Results agree with light-cone string field theory predictions.

Abstract

We extend the study of the quantum mechanics of BMN gauge theory to the sector of three scalar impurities at one loop and all genus. The relevant matrix elements of the non-planar one loop dilatation operator are computed in the gauge theory basis. After a similarity transform the BMN gauge theory prediction for the corresponding piece of the plane wave string Hamiltonian is derived and shown to agree with light-cone string field theory. In the three-impurity sector single string states are unstable for the decay into two-string states at leading order in g_2. The corresponding decay widths are computed.