Supergeometry

Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel of many classical and quantum field theories involving odd fields, e.g., SUSY field theory, BRST theory, or supergravity.

Supergeometry is formulated in terms of ${\displaystyle \mathbb {Z} _{2}}$-graded modules and sheaves over ${\displaystyle \mathbb {Z} _{2}}$-graded commutative algebras (supercommutative algebras). In particular, superconnections are defined as Koszul connections on these modules and sheaves. However, supergeometry is not particular noncommutative geometry because of a different definition of a graded derivation.

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