BMN Operators from Wilson Loop

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.

17 pages, v2: arguments on the correction terms expanded, references added, v3: minor corrections, to appear in JHEP

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• Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual
• Small deformations of supersymmetric Wilson loops and open spin-chains
• A Semiclassical String Description of Wilson Loop with Local Operators
• Holography of Wilson-Loop Expectation Values with Local Operator Insertions
• Correlation function of null polygonal Wilson loops with local operators
• Exact 1/4 BPS Loop - Chiral Primary Correlator
• On correlation functions of Wilson loops, local and non-local operators
• Holography of Non-relativistic String on AdS5xS5
• Non-relativistic String and D-branes on AdS_5 x S^5 from Semiclassical Approximation
• Circular loop operators in conformal field theories
• BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory
• Loop Equation in D=4, N=4 SYM and String Field Equation on AdS_5 \times S^5