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


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.

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Correspondence to Paul Mansfield.

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ArXiv ePrint: 1712.04760

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Curry, C., Mansfield, P. Intersection of world-lines on curved surfaces and path-ordering of the Wilson loop. J. High Energ. Phys. 2018, 81 (2018).

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  • Bosonic Strings
  • Long strings
  • Wilson, ’t Hooft and Polyakov loops
  • Field Theories in Lower Dimensions