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.
Highlights
In the year 1974 Scherk and Schwarz [1] suggested that the massless spin-2 closed string excitation has a natural interpretation in terms of the graviton, i.e. the field quantum of gravity
In this work we have begun to investigate in what way ghost-free bimetric gravity, which around Minkowski backgrounds propagates a massless graviton as well as an additional massive spin-2 field, can arise from string theory as an effective field theory
As we discussed in this work, massive spin-2 states arise in string theory in several ways
Summary
In the year 1974 Scherk and Schwarz [1] suggested that the massless spin-2 closed string excitation has a natural interpretation in terms of the graviton, i.e. the field quantum of gravity. In this work we will follow an alternative path, namely we will regard the massive spin-2 state of bimetric gravity as a particular open string excitation It was already discussed in [40] that bimetric gravity finds a very natural realization in D-brane models, where the standard massless graviton lives as closed string in the higher dimensional bulk, but the massive spin-2 state arises as open string on the world-volume of a D3-brane. The relevant worldsheet topology is that of a disk, whose boundary is attached to the brane worldvolume, with the vertex operators inserted in the bulk or on the boundary for closed or open strings respectively In this way, we compute, using generic boundary conditions, the superstring three-point amplitude describing the scattering of one massless closed string graviton and two massive open string spin-2 states.
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