https://doi.org/10.1140/epjc/s10052-015-3834-6
Regular Article - Theoretical Physics
BPS Wilson loops in Minkowski spacetime and Euclidean space
1
Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Rd, Beijing, 100049, China
2
Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, 19B Yuquan Rd, Beijing, 100049, China
* e-mail: jjzhang@ihep.ac.cn
Received:
27
May
2015
Accepted:
9
December
2015
Published online:
21
December
2015
We give evidence that spacelike BPS Wilson loops do not exist in Minkowski spacetime. We show that spacelike Wilson loops in Minkowski spacetime cannot preserve any supersymmetries, in 
super Yang–Mills theory, 
super Chern–Simons-matter theory, and
Aharony–Bergman–Jafferis–Maldacena theory. We not only show this using infinite straight lines and circles as examples, but also we give proofs for general curves. We attribute this to the conflicts of the reality conditions of the spinors. However, spacelike Wilson loops do exist in Euclidean space. There are both BPS Wilson loops along infinite straight lines and circular BPS Wilson loops. This is because the reality conditions of the spinors are lost after Wick rotation. The result is reasonable in view of the AdS/CFT correspondence.
© The Author(s), 2015
