Light-like Wilson loop correlators

TL;DR

The work extends the standard Wilson loop/amplitude duality by studying correlation functions of multiple light-like Wilson loops in planar N=4 SYM, employing a twistor-space formalism and an R-invariant framework to organize perturbative contributions. It provides explicit Abelian (U(1)) results at leading order, showing a natural exponentiation and a generalized bar_Q equation, and it delineates the structure of leading SU(N) contributions in terms of products of basic two-loop building blocks f_{n_i,n_j}. The paper also develops a comprehensive tree-level super Wilson loop analysis (NMHV, N^2MHV, N^3MHV) and derives practical Feynman rules in R-invariant form, enabling systematic computation of higher-MHV correlators. Collectively, these results establish a scalable perturbative program for multi-loop, multi-Wilson-loop observables and set the stage for further exploration of BCFW-type recursions, loop integrands, and potential underlying geometric structures in this generalized setting.

Abstract

It is well-known that the expectation values of null polygonal Wilson loops computed in planar \(\mathcal{N}=4\) super Yang-Mills theory are dual to MHV amplitudes in that theory, and moreover that the duality can be extended to higher helicity sectors through the introduction of super Wilson loops. In this first of a series of papers, we investigate the natural generalisation posed by correlation functions of multiple light-like loop operators, both in the bosonic case and in the case of super Wilson loops. Explicit calculations are presented in several cases and we verify that, in the Abelian theory, these objects obey a natural generalisation of the \(\bar{Q}\)-equation which relates different loop orders, kinematic configurations and Grassmann sectors.

Figures (13)

• Figure 1: Feynman diagram contribution to the correlator of two squares in the Abelian theory.
• Figure 2: Feynman diagram contribution to the connected part of the correlator of two squares and one pentagon in the non-Abelian theory.
• Figure 3: A general twistor Wilson loop diagram with $n$ propagators attached to the Lagrangian line $X=(Z_A,Z_B)$; here we label the integration variables associated to the insertion point of the propagators on the twistor lines.
• Figure 4: A general twistor diagram with $n$ insertions on the Lagrangian line $X=(Z_A,Z_B)$, which differs from Fig. \ref{['nvertexdiag']} by some arbitrary permutation of the attachments to the Lagrangian line.
• Figure 5: Two N$^2$MHV tree diagrams where the propagators run between the same twistor lines but with the order of insertion on the lines switched. While one of these diagrams would be colour suppressed in the SU$(N)$ theory for a single Wilson loop, for two Wilson loops both diagrams are planar and can be combined as a single integral, resulting in the disappearance of shifted twistors.