BMN Operators from Wilson Loop

TL;DR

This paper demonstrates that BMN operators in N=4 super Yang-Mills theory can be derived from the expansion of a specific Wilson loop, establishing a connection between gauge theory operators and string theory constructs.

Contribution

It shows how to obtain BMN operators from Wilson loop expansions in four-dimensional N=4 SYM, linking gauge theory and string field concepts.

Findings

BMN operators emerge from Wilson loop expansions.

The phase factors of BMN operators are correctly reproduced.

The Wilson loop corresponds to string field in the dual theory.

Abstract

We show that the BMN operators arise from the expansion of the Wilson loop in four-dimensional N=4 super Yang-Mills theory. The Wilson loop we consider is obtained from ``dimensional reduction'' of ten-dimensional N=1 super Yang-Mills theory, and it contains six scalar fields as well as the gauge field. We expand the Wilson loop twice. First we expand it in powers of the fluctuations around a BPS loop configuration. Then we further expand each term in the result of the first step in powers of the scalar field Z associated with the BPS configuration. We find that each operator in this expansion with large number of Z is the BMN operator. The number of fluctuations corresponds to the number of impurities, and the phase factor of each BMN operator is supplied correctly. We have to impose the BPS condition on the loop for obtaining the complete form of the BMN operators including the correction terms with \bar Z. Our observation suggests the correspondence between the Wilson loop and the string field.