Killing vector fields and harmonic superfield theories (Q2924907)

This paper assumes familiarity with the Berezin-Kostant-Leites definition of supermanifolds and their morphisms in terms of sheaves ([\textit{D. A. Leites}, Usp. Mat. Nauk 35, No. 1(211), 3--57 (1980; Zbl 0439.58007)]) and generalizes the harmonic action functional to semi-Riemannian supergeometry in this framework. In physics the field theories defined by this action are known as supersymmetric sigma models. It is shown that Killing vector fields on both the domain and the target manifold entail supersymmetries of the harmonic action and hence Noether theorems. In the appendix the author proves the equivalence of five different characterizations of Killing vector fields on supermanifolds.