Strings in Bimetric Spacetimes

TL;DR

This paper introduces a two-dimensional nonlinear sigma model coupling matter fields to bimetric Horava gravity, deriving quantum consistency conditions that lead to gravitational field equations and an emergent Lorentz symmetry.

Contribution

It develops a novel sigma model framework for strings in bimetric spacetimes, connecting quantum worldsheet invariance to target space gravitational dynamics.

Findings

Derivation of beta-functionals for bimetric fields.

Emergence of Einstein gravity in the single metric limit.

Identification of a unique massless spin-two excitation.

Abstract

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.