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 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.

Extracting Bigravity from String Theory

“…However, the absence of a second diffeomorphism invariance in our string setup should not come as a great surprise, since in string theory it is absolutely not guaranteed, or even clear, that each massive spin-2 mode should also come with its own diffeomorphism symmetry. Whether this could be the case for the massive closed string excitations, which as afore mentioned come from a double copy construction of a massive Proca field, will be clarified in [29]. As a final comment, let us note that the tree-level disk amplitude with two massless closed and one massive open string state in the external legs is an interesting future computation, given the absence of such cubic interaction terms in bimetric theory around Minkowski backgrounds [29].…”

“…Whether this could be the case for the massive closed string excitations, which as afore mentioned come from a double copy construction of a massive Proca field, will be clarified in [29]. As a final comment, let us note that the tree-level disk amplitude with two massless closed and one massive open string state in the external legs is an interesting future computation, given the absence of such cubic interaction terms in bimetric theory around Minkowski backgrounds [29].…”

“…Because of these reasons, we decided to investigate in this work the open string option for the massive spin-2 field of bimetric gravity, its corresponding covariant string vertex operator and the (massive) 2 -massless, i.e (open) 2closed, and also the (massive) 3 , i.e (open) 3 , string scattering amplitudes in great detail. The closed string option for the massive spin-2 excitation and its effective action will be discussed in a future publication [29].…”

“…propagating the correct number of dof in the critical dimension in accordance wth table 1. Motivated by a recent interpretation of the ghost spin-2 mode within Eistein+Weyl 2 supergravity as precisely this massive spin-2 brane state [34], and given that the sum of Weyl 2 gravity and infinite higher-derivative terms has been shown to be classically equivalent to ghost-free bimetric theory (for a large class of solutions of the latter) [35], we choose to identify M µν with the former case in the present paper and are currently investigating further options in [29]. Comparing the mass-squared (3.2) of the string state with Fierz-Pauli mass (2.13) as predicted by ghost-free bimetric theory, we also identify…”

“…Actually, a massive spin-2 excitation can occur both in the massive closed string sector and also as a massive open string state describing D-brane excitations in type II theories. In the first case of a massive closed string spin-2 excitation, one could extract bimetric gravity as a double copy from two open string sectors [29]. This option would be in close analogy to the well-known double copy construction of Einstein (super) gravity as product of two open string Yang-Mills gauge theories, cf.…”