  We put forward a two-dimensional nonlinear sigma model that couples (bosonic)
matter fields to topological Horava gravity on a nonrelativistic worldsheet. In
the target space, this sigma model describes classical strings propagating in a
curved spacetime background, whose geometry is described by two distinct metric
fields. We evaluate the renormalization group flows of this sigma model on a
flat worldsheet and derive a set of beta-functionals for the bimetric fields.
Imposing worldsheet Weyl invariance at the quantum level, we uncover a set of
gravitational field equations that dictate the dynamics of the bimetric fields
in the target space, where a unique massless spin-two excitation emerges. When
the bimetric fields become identical, the sigma model gains an emergent Lorentz
symmetry. In this single metric limit, the beta-functionals of the bimetric
fields reduce to the Ricci flow equation that arises in bosonic string theory,
and the bimetric gravitational field equations give rise to Einstein's gravity.
