The principle of relative locality is a generalization of the principle of relativity in which even locality – the coincidence of events – is no longer absolute, and each observer has a different notion of spacetime. This is achieved by allowing (energy-)momentum space to be curved independently of spacetime. Phase space is the only truly invariant structure, that is, independent of the observer. This principle has recently been implemented in metastring theory, a new formulation of string theory in which the strings propagate on the entire phase space. In addition to the symplectic form \omega, the metastring phase space possesses a polarization metric \eta, which specifies how phase space is decomposed into spacetime and momentum space, and a generalized metric H, which encodes the independent curvatures of these spaces. Our aim in this essay is to make the first step towards understanding this so-called metageometry, postulated to uniquely define a generalization of Einstein gravity which we refer to as metagravity. This is accomplished by conjuring some “string magic”. If we ask the strings of string theory what kind of background spacetime they are willing to propagate on, their reply, compelled by mathematical consistency alone, is that the spacetime metric must satisfy Einstein's equations of general relativity. Deriving the metagravity equations is thus simply a matter of posing the same question in metastring theory. More precisely, we perturb the background fields and require that the resulting worldsheet theory remains a conformal field theory. Using this method of conformal deformations, we find linearized equations of motion for the perturbations.

MSc Thesis