Geometry of N=1 Super Yang-Mills Theory in Curved Superspace

Anatoly Konechny, Albert Schwarz

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1 Citation (Scopus)


We give a new description of N = 1 super Yang-Mills (SYM) theory in curved superspace. It is based on the induced geometry approach to a curved superspace in which it is viewed as a surface embedded into C4|2. The complex structure on C4z.sfnc;2 supplied with a standard volume element induces a special Cauchy-Riemann (SCR)-structure on the embedded surface. We give an explicit construction of SYM theory in terms of intrinsic geometry of the superspace defined by this SCR-structure and a CR-bundle over the superspace. We write a manifestly SCR-covariant Lagrangian for SYM coupled with matter. We also show that in a special gauge our formulation coincides with the standard one which uses Lorentz connections. Some useful auxiliary results about the integration over surfaces in superspace are obtained.
Original languageEnglish
Pages (from-to)97-110
Number of pages14
JournalJournal of Geometry and Physics
Issue number2
Publication statusPublished - Sept 1997


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