Strings in bimetric spacetimes

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.

Automated summary

The study presents a two-dimensional nonlinear Sigma model that describes classical strings propagating in a curved spacetime background, with derived beta-functionals for the bimetric fields. Imposing worldsheet Weyl invariance at the quantum level reveals a set of gravitational field equations that dictate the dynamics of the bimetric fields in the target space.