One-Loop Soft Theorems via Dual Superconformal Symmetry

TL;DR

This work analyzes one-loop soft theorems in planar $\mathcal{N}=4$ SYM through finite infrared regulator order and subleading soft parameter order, deriving universal constraints from dual superconformal Ward identities. It bootstraps subleading $\log\delta$ terms and determines the complete infrared-finite subleading soft contribution for $n$-point MHV amplitudes using momentum twistors, while computing the subleading $\log\delta$ behaviour of six- and seven-point NMHV ratio functions to test universality across helicity sectors. The authors provide explicit, compact expressions for the infrared-finite subleading soft terms in MHV amplitudes and reveal sector-dependent universality in NMHV cases, supported by unitarity and twistorial techniques. The results advance understanding of how dual conformal symmetry constrains soft limits, with potential implications for amplitude bootstraps, twistorial methods, and higher-loop soft theorems in supersymmetric gauge theories.

Abstract

We study soft theorems at one loop in planar N=4 super Yang-Mills theory through finite order in the infrared regulator and to subleading order in the soft parameter δ. In particular, we derive a universal constraint from dual superconformal symmetry, which we use to bootstrap subleading log δ behaviour. Moreover, we determine the complete infrared-finite subleading soft contribution of n-point MHV amplitudes using momentum twistors. Finally, we compute the subleading log δ behaviour of one-loop NMHV ratio functions at six and seven points, finding that universality holds within but not between helicity sectors.

Figures (5)

• Figure 1: The four diagrams contributing to the infrared-divergent terms in the soft theorem at one loop.
• Figure 2: Two of the $3n{-}10$ diagrams contributing to the finite terms in the soft theorem at one loop.
• Figure 3: Solving for $x_j(p)$ clockwise around the polygon from $x_i$.
• Figure 4: Setting $x_3=0$ is compatible with eliminating $|1]$ and $|2]$.
• Figure 5: A generic two-mass easy box with massless corners $i$ and $j$ corresponding to the end edges of the internal gluon in the Wilson loop picture.