Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory

Details Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory

2011-10-06

arxiv.org/abs/1110.1373v2

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, 4 figures, minor changes, version to be published, report number added

Scientific paper

In previous investigations, it was found that four-sided polygonal light-like Wilson loops in ABJM theory calculated to two-loop order have the same form as the corresponding Wilson loop in N = 4 SYM at one-loop order. Here we study light-like polygonal Wilson loops with n cusps in planar three-dimensional Chern-Simons and ABJM theory to two loops. Remarkably, the result in ABJM theory precisely agrees with the corresponding Wilson loop in N = 4 SYM at one-loop order for arbitrary n. In particular, anomalous conformal Ward identites allow for a so-called remainder function of conformal cross ratios, which is found to be trivial at two loops in ABJM theory in the same way as it is trivial in N = 4 SYM at one-loop order. Furthermore, the result for arbitrary n obtained here, allows for a further investigation of a Wilson loop / amplitude duality in ABJM theory, for which non-trivial evidence was recently found by a calculation of four-point amplitudes that match the Wilson loop in ABJM theory.

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