We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkowski background respects wordline inversion symmetry, the particle approximation to modular invariance in string theory. This symmetry automatically yields a corresponding gravitational theory that is nonlocal, with the action containing infinite order differential operators. As a consequence, despite being a higher order derivative theory, it is ghost-free and has no degrees of freedom besides the massless spin-2 graviton of Einstein’s general relativity. By working in the linearised regime we show that the point-like singularities that afflict the (local) Einstein’s theory are smeared out.
Abel, S., Buoninfante, L., & Mazumdar, A. (2020). Nonlocal gravity with worldline inversion symmetry. Journal of High Energy Physics, 2020(1), Article 3. https://doi.org/10.1007/jhep01%282020%29003