Discretized Minimal Surface and the BDS Conjecture in N=4 Super Yang-Mills Theory at Strong Coupling

TL;DR

This paper numerically constructs minimal surfaces in AdS spacetime related to gluon scattering amplitudes in N=4 super Yang-Mills theory and tests the BDS conjecture at strong coupling.

Contribution

It provides a numerical analysis of minimal surfaces for multi-point amplitudes and verifies the BDS formula's predictions in a specific momentum configuration.

Findings

Numerical minimal surface areas agree with BDS conjecture predictions.

Area differences are independent of the remainder function.

Dependence on conformal boost parameters matches BDS formula.

Abstract

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(\geq 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.