Discretized minimal surface and the BDS conjecture in N=4 super-Yang-Mills theory at strong coupling

We construct numerically the minimal surface in AdS spacetime surrounded by the light-like segments, which are dual to the 4, 6 and 8-point gluon scattering amplitudes in N=4 super-Yang-Mills theory. We evaluate the area of the minimal surface in the radial cut-off regularization and compare these areas with the formula conjectured by Bern, Dixon and Smirnov (BDS), which is modified by the remainder function of cross-ratios of external momenta for n(≥6)-point amplitudes. In our momentum configuration cross-ratios are constant. We calculate the difference of areas with different conformal boost parameters, which is independent of the remainder function, and find that its dependence on the boost parameter is numerically consistent with the BDS formula.