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

A. Konechny·A. Schwarz
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Abstract

We give a new description of N=1 super Yang-Mills 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 C(4|2). The complex structure on C(4|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.

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A. Konechny, A. Schwarz. 1996-09-12. Geometry of N=1 Super Yang-Mills Theory in Curved Superspace. https://doi.org/10.1016/s0393-0440(96)00050-2

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