Impurities Near the Light Cone

Abstract

The lightlike Wilson line cusp underlies the Sudakov double logarithm and is a central ingredient in gauge-theory factorization. We ask what replaces this behavior for general conformal line defects in Lorentzian signature. We argue that, when the defects admit local endpoint operators, the cusp anomalous dimension has a finite large-boost limit fixed by the scaling dimensions of the corresponding defect-creation operators. We further analyze the distinct analytic continuations of the cusp, elucidate their physical interpretations, and derive a positivity condition on the Lorentzian cusp anomalous dimension. We test these predictions in several perturbative examples, including pinning-field defects and spin impurities, and discuss their possible implications for gauge theories.