Conclusion
In the present article we have considered two supersymmetric non-abelian gauge theories in the presence of an external magnetic field. In has been shown that the effect of the magnetic field breaks suppersymmetry at the one-loop level; however, if supersymmetry is already broken spontaneously at the tree level, then the magnetic field effect does not restore it at the one-loop level. These facts could be used in SUSY GUT models (which are used to describe the early universe), to study phase transition in those models.
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Roy, P. A note on supersymmetry and magnetic fields. Czech J Phys 34, 516–519 (1984). https://doi.org/10.1007/BF01595705
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DOI: https://doi.org/10.1007/BF01595705