Nonlocal gravity with worldline inversion symmetry
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Springer
Received: November 26, 2019 Accepted: November 26, 2019 Published: January 2, 2020
Steven Abel,a Luca Buoninfanteb and Anupam Mazumdarc a
Institute for Particle Physics Phenomenology, Durham University, South Road, Durham, U.K. b INFN — Sezione di Napoli, Gruppo collegato di Salerno, Fisciano, Salerno I-84084, Italy c Van Swinderen Institute, University of Groningen, Groningen 9747 AG, The Netherlands
E-mail: [email protected], [email protected], [email protected] Abstract: 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. Keywords: String Field Theory, Models of Quantum Gravity, Spacetime Singularities, Effective Field Theories ArXiv ePrint: 1911.06697
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)003
JHEP01(2020)003
Nonlocal gravity with worldline inversion symmetry
Contents 1
2 Scalar propagator and worldline inversion symmetry 2.1 Propagator in coordinate space
4 6
3 Nonlocal gravitational theory 3.1 Graviton propagator with worldline inversion symmetry
6 8
4 Nonsingular gravitational potential
9
5 Conclusions
1
11
Introduction
Einstein’s general relativity (GR) is the most widely studied theory of gravity, and its predictions have been tested to very high precision in the infrared (IR) regime, i.e. at large distances and late times [1]. Despite passing these tests, there are unsolved conceptual problems which indicate that Einstein’s GR is merely an effective field theory of gravitation: it works very well at low energy but breaks down in the ultraviolet (UV). Indeed √ at the classical level the Einstein-Hilbert Lagrangian, −gR, suffers from the presence of blackhole and cosmological singularities [2] (implying problems in the short-distance regime), while at the quantum level it is non-renormalisable from a perturbative point of view (implying problems in the high-energy regime) [3, 4]. Therefore there is a consensus that ultimately GR will need to be extended. One possible extension of GR is to add terms that are quadratic in curvature, such as R2 and Rµν Rµν . The resulting actions are power counting renormalisable as shown in ref. [5]. However they are still non-physical because of the presence of a massive spin2 ghost degree of freedom which classically causes Hamiltonian instabilities, and which quantum mechanically breaks the unitarity condition of the S-matrix. The appearance of gho
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