  We construct the Komar integral for axion-dilaton gravity using Wald's
formalism and momentum maps and we use it to derive a Smarr relation for
stationary axion-dilaton black holes. While the Wald-Noether 2-form charge is
not invariant under SL(2,R) electric-magnetic duality transformations because
Wald's formalism does not account for magnetic charges and potentials, the
Komar integral constructed with it turns out to be invariant and, in more
general theories, it will be fully symplectic invariant. We check the Smarr
formula obtained with the most general family of static axion-dilaton black
holes.
