Two-loop five-point all-plus helicity Yang-Mills amplitude

Abstract

We re-compute the recently derived two-loop five-point all plus Yang-Mills amplitude using Unitarity and Recursion. Recursion requires augmented recursion to determine the sub-leading pole. Using these methods the simplicity of this amplitude is understood.

Two-loop gravity amplitudes from four dimensional unitarity

“…In D-dimensional unitarity the cuts are computed in D = 4 − 2ǫ dimensions where, typically, the components of the cuts are considerably more complicated than in four dimensions. In [4] it was demonstrated that fourdimensional unitarity techniques [5,6] blended with a knowledge of the singular structure of the amplitude could reproduce this form in a straightforward way. The four-dimensional approach was also used to calculate the six-point amplitude [7,8] which was subsequently verified [9].…”

Heptagons from the Steinmann cluster bootstrap

“…Aspects of this approach have been applied to theories such as quantum chromodynamics at one loop [2][3][4] and more recently at two loops [5][6][7]. However, the most powerful applications to date have been to the planar limit of N = 4 super-YangMills (SYM) theory in four dimensions [8,9].…”

“…Therefore the singular behavior of the sixpoint amplitude is controlled by a single coefficient function, which we denote by U 6 and JHEP02(2017)137 whose limiting behavior takes an especially simple form. 6 Up to power-suppressed terms, the limit of U 6 was found to be a polynomial in log(uw/v), whose coefficients are rational linear combinations of zeta values, and whose overall weight is 2L. Here, u, v, and w are the three dual conformal invariant cross ratios for the hexagon, whose expressions in terms of six-point kinematics are…”

“…Therefore the initial number of free parameters at L loops, shown in table 2, is given by 15 times the entry in table 1 that counts the total number of Steinmann heptagon symbols of weight 2L. 5 We then impose the heptagon NMHV final entry condition discussed in subsection 4.1. Similarly to the NMHV hexagon case [35], the list of allowed final entries in eq.…”

“…Similarly to the NMHV hexagon case [35], the list of allowed final entries in eq. (4.1) can be translated into relations between the 42 different {k − 1, 1} coproduct components for each of the 15 functions multiplying the independent R-invariants, for a total of 42×15 5 If we had imposed dihedral symmetry first, we would have had only three independent functions E0, E12 and E14 to parametrize, each with some dihedral symmetry, and there would have been fewer than 3 times the number of independent Steinmann heptagon symbols in the first line of the table. This part of the computation is not a bottleneck either way.…”