Extracting Bigravity from String Theory

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 there can be a match between the string and the bimetric theory prediction in the case of two-derivative interactions of the graviton with two massive spin-2 states, unlike massive spin-2 cubic self-interactions, a fact that we analyze and interpret. We conclude with a mention of future investigations.

Holographic consistency and the sign of the Gauss-Bonnet parameter

“…The hope is that such effective theories can in fact be embedded into string theory. For examples, attempts have been made to embed massive gravity [17], bimetric gravity [18], Hořava gravity [19] and Lifshitz gravity [20] in string theory, which provide some justifications for their applications in the literature. However, not all effective field theories can be embedded into string theory, as expressed by the "Swampland Conjecture" [21,22].…”

On massive spin-2 in the Fradkin-Vasiliev formalism. II. General massive case

“…• Our results are in complete agreement with those of [28] obtained in the metric-like formalism. We also compared our results with the ones obtained recently in the stringy context [41].…”

“…Note that for this vertex the two derivative part for bigravity [46] and from (super)string [41] coincides (here symmetric tensor G µν corresponds to the massless graviton):…”

“…Recently,, an interesting paper [41] appeared, where the cubic vertices for massive spin 2 self-interaction as well as its interaction with massless graviton were elaborated in the stringy context. The massive spin 2 comes from the first massive level of open bosonic or superstring, while massless graviton comes from the closed (super)string.…”

Multigravity and the cosmological constant

“…An infinite number of fields would indicate extended structure/nonlocality in whatever fundamental theory underlies (9) viewed as an effective theory. There have been some attempts to extract massive gravity or bigravity from string theory, e.g [17], but so far they remain inconclusive.…”