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On Duality in $mathcal{N}=2$ supersymmetric Liouville Theory

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 نشر من قبل Yu Nakayama
 تاريخ النشر 2020
  مجال البحث
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 تأليف Yu Nakayama




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Similarly to the bosonic Liouville theory, the $mathcal{N}=2$ supersymmetric Liouville theory was conjectured to be equipped with the duality that exchanges the superpotential and the Kahler potential. The conjectured duality, however, seems to suffer from a mismatch of the preserved symmetries. More than fifteen years ago, when I was a student, my supervisor Tohru Eguchi gave a beautiful resolution of the puzzle when the supersymmetry is enhanced to $mathcal{N}=4$ based on his insight into the underlying geometric structure of the $A_1$ singularity. I will review his unpublished but insightful idea and present our attempts to extend it to more general cases.



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