Duality between Correlation Functions and Wilson Loops in Gauge Theory from Effective Field Theory

In this Letter, we initiate a systematic study of the n-point correlation functions (CFs) 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 nonconformal 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 nonvanishing β function of QCD. As a stringent check, we verify that our result satisfies the anomalous conformal Ward identities and that its leading transcendental term reproduces the known correlation function in N=4 SYM to three loops. Our results are easily generalized to the multipoint case, offering a powerful tool for future applications of SCET to the study of the fundamental structure of gauge theories.