We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudo-forms and integral forms) and the extended Cartan calculus are discussed. We then introduce Picture Changing Operators. We provide several examples of computation of PCO's acting on different type of forms. We illustrate also the action of the η operator, crucial ingredient to define the interactions of super Chern-Simons theory. Then, we discuss the action for super Chern-Simons theory on any supermanifold, first in the factorized form (3-form × PCO) and then, we consider the most general expression. The latter is written in term of psuedo-forms containing an infinite number of components. We show that the free equations of motion reduce to the usual Chern-Simons equations yielding the proof of the equivalence between the formulations at different pictures of the same theory. Finally, we discuss the interaction terms. They require a suitable definition in order to take into account the picture number. That implies the construction of a 2-product which is not associative that inherits an A ∞ algebra structure. That shares several similarities with a recent construction of a super string field theory action by

We study supersymmetric Wilson loops from a geometrical perspective. To this end, we propose a new formulation of these operators in terms of an integral form associated to the immersion of the loop into a supermanifold. This approach provides a unifying description of Wilson loops preserving different sets of supercharges, and clarifies the flow between them. Moreover, it allows to exploit the powerful techniques of super-differential calculus for investigating their symmetries.As remarkable examples, we discuss supersymmetry and kappa-symmetry invariance.

This is a companion paper of a long work appeared in [C. Cremonini and P. Grassi, Pictures from super Chern-Simons theory, J. High Energy Phys. 03 (2020) 043] discussing the super-Chern-Simons theory on supermanifolds. Here, it is emphasized that the Batalin-Vilkovisky formalism is naturally formulated using integral forms for any supersymmetric and supergravity models and we show how to deal with A ∞ algebras emerging from supermanifold structures.