TL;DR
This paper investigates the properties of Abrikosov-Nielsen-Olesen strings in N=2 supersymmetric QED, examining how small perturbations breaking supersymmetry affect string tension and BPS saturation.
Contribution
It analyzes the impact of quadratic superpotential perturbations on the BPS status and tension of Abrikosov strings in N=2 supersymmetric QED.
Findings
Abrikosov string is 1/2-BPS saturated in N=2 supersymmetric QED.
Small perturbations break N=2 to N=1 supersymmetry, removing BPS saturation.
The tension difference between non-BPS and BPS strings is negative at first order.
Abstract
We study the Abrikosov-Nielsen-Olesen string in N=2 supersymmetric QED with N=2-preserving superpotential, in which case the Abrikosov string is found to be 1/2-BPS saturated. Adding a quadratic small perturbation in the superpotential breaks N=2 supersymmetry to N=1 supersymmetry. Then the Abrikosov string is no longer BPS saturated. The difference between the string tensions for the non-BPS and BPS saturated situation is found to be negative to the first order of the perturbation parameter.
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