Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory

Details Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory

2010-04-01

arxiv.org/abs/1004.0226v3

JHEP 1008:032,2010

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, many figures; v2: references added, minor changes; v3: references added, sign error fixed and note added

Scientific paper

10.1007/JHEP08(2010)032

We study light-like polygonal Wilson loops in three-dimensional Chern-Simons and ABJM theory to two-loop order. For both theories we demonstrate that the one-loop contribution to these correlators cancels. For pure Chern-Simons, we find that specific UV divergences arise from diagrams involving two cusps, implying the loss of finiteness and topological invariance at two-loop order. Studying those UV divergences we derive anomalous conformal Ward identities for n-cusped Wilson loops which restrict the finite part of the latter to conformally invariant functions. We also compute the four-cusp Wilson loop in ABJM theory to two-loop order and find that the result is remarkably similar to that of the corresponding Wilson loop in N=4 SYM. Finally, we speculate about the existence of a Wilson loop/scattering amplitude relation in ABJM theory.

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