Simplicity of Polygon Wilson Loops in N=4 SYM Export

@article{citeulike:6015837, abstract = {Wilson loops with lightlike polygonal contours have been conjectured to be equivalent to MHV scattering amplitudes in N=4 super Yang-Mills. We compute such Wilson loops for special polygonal contours at two loops in perturbation theory. Specifically, we concentrate on the remainder function R, obtained by subtracting the known ABDK/BDS ansatz from the Wilson loop. First, we consider a particular two-dimensional eight-point kinematics studied at strong coupling by Alday and Maldacena. We find numerical evidence that R is the same at weak and at strong coupling, up to an overall, coupling-dependent constant. This suggests a universality of the remainder function at strong and weak coupling for generic null polygonal Wilson loops, and therefore for arbitrary MHV amplitudes in N=4 super Yang-Mills. We analyse the consequences of this statement. We further consider regular n-gons, and find that the remainder function is linear in n at large n through numerical computations performed up to n=30. This reproduces a general feature of the corresponding strong-coupling result.}, archivePrefix = {arXiv}, author = {Brandhuber, Andreas and Heslop, Paul and Khoze, Valentin V. and Travaglini, Gabriele}, citeulike-article-id = {6015837}, citeulike-linkout-0 = {http://arxiv.org/abs/0910.4898}, citeulike-linkout-1 = {http://arxiv.org/pdf/0910.4898}, day = {26}, eprint = {0910.4898}, keywords = {polygon, wilson\_loops}, month = {Oct}, posted-at = {2009-10-27 13:47:22}, priority = {2}, title = {Simplicity of Polygon Wilson Loops in N=4 SYM}, url = {http://arxiv.org/abs/0910.4898}, year = {2009} }

TY - JOUR ID - citeulike:6015837 L3 - citeulike-article-id:6015837 N2 - Wilson loops with lightlike polygonal contours have been conjectured to be equivalent to MHV scattering amplitudes in N=4 super Yang-Mills. We compute such Wilson loops for special polygonal contours at two loops in perturbation theory. Specifically, we concentrate on the remainder function R, obtained by subtracting the known ABDK/BDS ansatz from the Wilson loop. First, we consider a particular two-dimensional eight-point kinematics studied at strong coupling by Alday and Maldacena. We find numerical evidence that R is the same at weak and at strong coupling, up to an overall, coupling-dependent constant. This suggests a universality of the remainder function at strong and weak coupling for generic null polygonal Wilson loops, and therefore for arbitrary MHV amplitudes in N=4 super Yang-Mills. We analyse the consequences of this statement. We further consider regular n-gons, and find that the remainder function is linear in n at large n through numerical computations performed up to n=30. This reproduces a general feature of the corresponding strong-coupling result. TI - Simplicity of Polygon Wilson Loops in N=4 SYM KW - polygon KW - wilson_loops AU - Brandhuber, Andreas AU - Heslop, Paul AU - Khoze, Valentin AU - Travaglini, Gabriele PY - 2009/Oct/26/ UR - http://arxiv.org/abs/0910.4898 ER -