arXiv:1712.04760v2 [hep-th] 9 Feb 2018 Prepared for submission to JHEP Intersection of world-lines on curved surfaces and path-ordering of the Wilson loop Chris Curry and Paul Mansfield Centre for Particle Theory, University of Durham, Durham DH1 3LE, UK E-mail:p.r.w.mansfield@durham.ac.uk, c.h.curry@durham.ac.uk 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 pre- viously used to represent the Abelian Wilson loop as a tensionless string. We also describe a supersymmetric generalisation. Keywords:Field Theories in Lower Dimensions, Bosonic Strings
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