Exploring Reggeon bound states in strongly-coupled $$ \mathcal{N} $$ = 4 super Yang-Mills

The multi-Regge limit of scattering amplitudes in strongly-coupled $$ \mathcal{N} $$ N = 4 super Yang-Mills is described by the large mass limit of a set of thermodynamic Bethe ansatz (TBA) equations. A non-trivial remainder function arises in this setup in certain kinematical regions due to excitations of the TBA equations which appear during the analytic continuation into these kinematical regions. So far, these analytic continuations were carried out on a case-by-case basis for the six- and seven-gluon remainder function. In this note, we show that the set of possible excitations appearing in any analytic continuation in the multi-Regge limit for any number of particles is rather constrained. In particular, we show that the BFKL eigenvalue of any possible Reggeon bound state is a multiple of the two-Reggeon BFKL eigenvalue appearing in the six-gluon case.

The three-loop MHV octagon from $$ \overline{Q} $$ equations

The $$ \overline{Q} $$ Q ¯ equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory. By using the $$ \overline{Q} $$ Q ¯ equations, we compute the symbol of the first MHV amplitude with algebraic letters — the three-loop 8-point amplitude (or the octagon remainder function) — in this theory. The symbol alphabet for this amplitude consists of 204 independent rational letters and shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.

The two-loop remainder function for eight and nine particles

Two-loop MHV amplitudes in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang Mills theory are known to exhibit many intriguing forms of cluster-algebraic structure. We leverage this structure to upgrade the symbols of the eight- and nine-particle amplitudes to complete analytic functions. This is done by systematically projecting onto the components of these amplitudes that take different functional forms, and matching each component to an ansatz of multiple polylogarithms with negative cluster-coordinate arguments. The remaining additive constant can be determined analytically by comparing the collinear limit of each amplitude to known lower-multiplicity results. We also observe that the nonclassical part of each of these amplitudes admits a unique decomposition in terms of a specific A3 cluster polylogarithm, and explore the numerical behavior of the remainder function along lines in the positive region.

Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

Form factors, as quantities involving both local operators and asymptotic particle states, contain information of both the spectrum of operators and the on-shell amplitudes. So far the studies of form factors have been mostly focused on the large Nc planar limit, with a few exceptions of Sudakov form factors. In this paper, we discuss the systematical construction of full color dependent form factors with generic local operators. We study the color decomposition for form factors and discuss the general strategy of using on-shell unitarity cut method. As concrete applications, we compute the full two-loop non-planar minimal form factors for both half-BPS operators and non-BPS operators in the SU(2) sector in $$ \mathcal{N} $$ N = 4 SYM. Another important aspect is to investigate the color-kinematics (CK) duality for form factors of high-length operators. Explicit CK dual representation is found for the two-loop half-BPS minimal form factors with arbitrary number of external legs. The full-color two-loop form factor result provides an independent check of the infrared dipole formula for two-loop n-point amplitudes. By extracting the UV divergences, we also reproduce the known non-planar SU(2) dilatation operator at two loops. As for the finite remainder function, interestingly, the non-planar part is found to contain a new maximally transcendental part beyond the known planar result.

Evaluating the six-point remainder function near the collinear limit

The simplicity of maximally supersymmetric Yang–Mills theory makes it an ideal theoretical laboratory for developing computational tools, which eventually find their way to QCD applications. In this contribution, we continue the investigation of a recent proposal by Basso, Sever and Vieira, for the nonperturbative description of its planar scattering amplitudes, as an expansion around collinear kinematics. The method of G. Papathanasiou, J. High Energy Phys.1311, 150 (2013), arXiv:1310.5735, for computing the integrals the latter proposal predicts for the leading term in the expansion of the six-point remainder function, is extended to one of the subleading terms. In particular, we focus on the contribution of the two-gluon bound state in the dual flux tube picture, proving its general form at any order in the coupling, and providing explicit expressions up to six loops. These are included in the ancillary file accompanying the version of this paper on the arXiv.