Intersection of world-lines on curved surfaces and path-ordering of the Wilson loop

Abstract

We study contact interactions for long world-lines on a curved surface, focusing on the average number of times two world-lines intersect as a function of their end-points. The result can be used to extend the concept of path-ordering, as employed in the Wilson loop, from a closed curve into the interior of a surface spanning the curve. Taking this surface as a string world-sheet yields a generalisation of the string contact interaction previously used to represent the Abelian Wilson loop as a tensionless string. We also describe a supersymmetric generalisation.

28 pages, 2 figures

References in corpus (5)

• Localisation in worldline pair production and lightfront zero-modes
• Pair production from residues of complex worldline instantons
• Delta-function Interactions for the Bosonic and Spinning Strings and the Generation of Abelian Gauge Theory
• QED as the tensionless limit of the spinning string with contact interaction
• Contact interactions between particle worldlines

Cited by in corpus (2)

• Non-perturbative Quantum Propagators in Bounded Spaces
• Steps Towards Generalization of Tensionless String Theory with Contact Interactions as Wilson loop of Non-Abelian Yang-Mills Theory