Strings in Bimetric Spacetimes

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.

42 pages; v2: minor clarifications; v3: minor clarifications, typos fixed; v4: minor typos

References in corpus (7)

• Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Extended Galilean symmetries of non-relativistic strings
• Interacting String Multi-verses and Holographic Instabilities of Massive Gravity
• The Galilean Superstring
• New Heat Kernel Method in Lifshitz Theories

Cited by in corpus (3)

• Aspects of Nonrelativistic Strings
• Renormalization of Supersymmetric Lifshitz Sigma Models
• A Loop Quantum Gravity Inspired Action for the Bosonic String and Emergent Dimensions at Large Scales