### References & Citations

# High Energy Physics - Theory

# Title: Strings in Bimetric Spacetimes

(Submitted on 30 Apr 2021 (v1), last revised 17 Sep 2021 (this version, v3))

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.

## Submission history

From: Ziqi Yan [view email]**[v1]**Fri, 30 Apr 2021 18:00:03 GMT (37kb,D)

**[v2]**Sun, 9 May 2021 20:11:38 GMT (38kb,D)

**[v3]**Fri, 17 Sep 2021 21:06:30 GMT (39kb,D)

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