Extracting Bigravity from String Theory

TL;DR

This paper investigates how ghost-free bimetric theory, involving two interacting metrics and a massive spin-2 field, can emerge from string theory by analyzing string scattering amplitudes and comparing effective actions.

Contribution

It demonstrates that string theory can produce the same two-derivative interaction terms as bimetric theory for a massive spin-2 field and graviton, up to numerical factors.

Findings

String and bimetric theories share similar interaction structures.

The effective actions from string theory match bimetric theory at lowest order.

Discrepancies in numerical coefficients are analyzed and discussed.

Abstract

The origin of the graviton from string theory is well understood: it corresponds to a massless state in closed string spectra, whose low-energy effective action, as extracted from string scattering amplitudes, is that of Einstein-Hilbert. In this work, we explore the possibility of such a string-theoretic emergence of ghost-free bimetric theory, a recently proposed theory that involves two dynamical metrics, that around particular backgrounds propagates the graviton and a massive spin-2 field, which has been argued to be a viable dark matter candidate. By choosing to identify the latter with a massive spin-2 state of open string spectra, we compute tree-level three-point string scattering amplitudes that describe interactions of the massive spin-2 with itself and with the graviton. With the mass of the external legs depending on the string scale, we discover that extracting the corresponding low-energy effective actions in four spacetime dimensions is a subtle but consistent process and proceed to appropriately compare them with bimetric theory. Our findings consist in establishing that string and bimetric theory provide to lowest order the same set of two-derivative terms describing the interactions of the massive spin-2 with itself and with the graviton, albeit up to numerical coefficient discrepancies, a fact that we analyze and interpret. We conclude with a mention of future investigations.