  The quantum theory of a massless spin two particle is strongly constrained by
diffeomorphism invariance, which is in turn implied by unitarity. We explicitly
exhibit the space-time diffeomorphism algebra of string theory, realizing it in
terms of world sheet vertex operators. Viewing diffeomorphisms as field
redefinitions in the two-dimensional conformal field theory renders the
calculation of their algebra straightforward. Next, we generalize the analysis
to combinations of space-time anti-symmetric tensor gauge transformations and
diffeomorphisms. We also point out a left-right split of the algebra combined
with a twist that reproduces the C-bracket of double field theory. We further
compare our derivation to an analysis in terms of marginal deformations as well
as vertex operator algebras.
