Correlation Function/Wilson Loop Duality in Gauge Theory from EFT

Abstract

In this Letter, we initiate a systematic study of the $n$-point correlation functions (CF) in gauge theories in the sequential light-cone (SLC) limit. Focusing on QCD, we formulate a factorization theorem for the CF of four vector currents in this limit using tools from soft-collinear effective field theory (SCET). This result unveils a duality between CF and Wilson loops in non-conformal field theories, according to which the singular structure of the CF is described by a null polygonal Wilson loop dressed by universal jet functions and current form factors, directly related to well-known ingredients in collider physics. We employ this new factorization theorem to obtain the singular terms of the four-point CF in QCD in the SLC limit up to three loops. This constitutes the first determination of terms beyond one loop and in particular determines, for the first time, conformal-symmetry-breaking terms induced by the non-vanishing $β$-function of QCD. As a stringent check, we verify that our result satisfies the anomalous conformal Ward identities and its leading-transcendental term reproduces the known correlation function in $\mathcal{N}=4$ SYM to three loops. Our results are easily generalized to the multi-point case, offering a powerful tool for future applications of SCET to the study of the fundamental structure of gauge theories.

Figures (3)

• Figure 1: Graphical depiction of $G(\{x\})$ in eq. \ref{['eq:JJJJ']} in the sequential light-cone limit. The dashed gray lines identify the light-cone directions approached by $y_i^\mu$.
• Figure 2: SCET modes in position space.
• Figure 3: Pictorial view of the factorization theorem for the sequential light-cone limit of the four-point correlation function. The Soft function, represented by the green polygon is a Wilson loop tracing the null polygon.