  Two-dimensional pure electrodynamics is mapped into two-dimensional gravity
in the first order formalism at classical and quantum levels. Due to the fact
that the degrees of freedom of these two theories do not match, we are enforced
to introduce extra fields from the beginning. These fields are introduced
through a BRST exact boundary term, so they are harmless to the physical
content of the theory. The map between electromagnetism and gravity fields
generate a non-trivial Jacobian, which brings extra features (but also harmless
to the physical content of the gravity theory) at quantum level.
