  We calculate the category of D-modules on the loop space of the affine line
in coherent terms. Specifically, we find that this category is derived
equivalent to the category of ind-coherent sheaves on the moduli space of rank
one de Rham local systems with a flat section. Our result establishes a
conjecture coming out of the 3d mirror symmetry program, which obtains new
compatibilities for the geometric Langlands program from rich dualities of QFTs
that are themselves obtained from string theory conjectures.
