Analogy between gravitational and gauge field Wilson line operators

Abstract The gauge field Wilson line operator is an important concept in the gauge field theory and can be derived from the nonlocal interaction. A similar analysis can be carried out for the nonlocal interaction in the curved space-time to obtain the gravitational Wilson line operator explicitly. In this paper we first review the connection between the nonlocal interaction and the gauge field Wilson line operator, then discuss the gravitational Wilson line operator. Finally, we prove the gauge invariance of the energy–momentum tensor to explore the effect of the Wilson line operator.