Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory

TL;DR

The paper investigates how conventional and dual superconformal symmetries constrain scattering amplitudes in planar N=4 SYM, showing that tree-level NMHV amplitudes are not fixed by these symmetries alone. It demonstrates that analytic properties, specifically the cancellation of spurious poles and correct multi-particle factorization, uniquely determine the NMHV tree amplitude as a sum of dual superconformal invariants R_{rst}. The authors then analyze loop corrections, showing that holomorphic anomalies induce a breakdown of dual Poincaré supersymmetry in the NMHV ratio function, while dual conformal symmetry remains intact for discontinuities; collinear limits and unitarity further constrain loop-level structures. The work highlights the delicate interplay between symmetry and analyticity in all-loop amplitudes and points to the need for a dual-space object that captures anomalies beyond the tree level. Together, these results advance understanding of how exact and anomalous symmetries shape the structure of N=4 SYM amplitudes and their loop corrections.

Abstract

In addition to the superconformal symmetry of the underlying Lagrangian, the scattering amplitudes in planar N=4 super-Yang-Mills theory exhibit a new, dual superconformal symmetry. We address the question of how powerful these symmetries are to completely determine the scattering amplitudes. We use the example of the NMHV superamplitudes to show that the combined action of conventional and dual superconformal symmetries is not sufficient to fix all the freedom in the tree-level amplitudes. We argue that the additional information needed comes from the study of the analytic properties of the amplitudes. The requirement of absence of spurious singularities, together with the correct multi-particle singular behavior, determines the unique linear combination of superinvariants corresponding to the n-particle NMHV superamplitude. The same result can be obtained recursively, by relating the n- and (n-1)-particle amplitudes in the singular collinear limit. We also formulate constraints on the loop corrections to the superamplitudes, following from the analytic behavior in the above limits. We then show that the holomorphic anomaly of the tree amplitudes leads to the breakdown of dual Poincare supersymmetry (which is equivalent to ordinary special conformal supersymmetry) of the ratio of the NMHV and MHV superamplitudes at one-loop level, but this anomaly does not affect dual conformal symmetry.

Figures (2)

• Figure 1: Diagrammatic representation of the dual superconformal invariant $R_{rst}$
• Figure 2: Three different configurations of superinvariants with cuts (dashed lines) corresponding to physical poles: generic case (a) and 'boundary' terms with $s=r+2$ (b) and $t=r-1$ (c).