We study a category of representations of the Lie algebras of vector fields on an affine algebraic variety X that admit a compatible action of the algebra of polynomial functions on X. We investigate two classes of simple modules in this category: gauge modules and Rudakov modules, and establish a covariant pairing between modules of these two types. We show that every module in this category, which is finitely generated over the algebra of functions, is projective, and state a conjecture that gauge modules exhaust all such modules. We give a proof of this conjecture when X is the affine space. This is a joint work with Slava Futorny, Jonathan Nilsson, Andre Zaidan, Colin Ingalls and Amir Nasr.