Abstract
We study scalar fields propagating on Euclidean dynamical triangulations (EDT). In this work we study the interaction of two scalar particles, and we show that in the appropriate limit we recover an interaction compatible with Newton's gravitational potential in four dimensions. Working in the quenched approximation, we calculate the binding energy of a two-particle bound state, and we study its dependence on the constituent particle mass in the non-relativistic limit. We find a binding energy compatible with what one expects for the ground state energy by solving the Schr\"{o}dinger equation for Newton's potential. Agreement with this expectation is obtained in the infinite-volume, continuum limit of the lattice calculation, providing non-trivial evidence that EDT is in fact a theory of gravity in four dimensions. Furthermore, this result allows us to determine the lattice spacing within an EDT calculation for the first time, and we find that the various lattice spacings are smaller than the Planck length, suggesting that we can achieve a separation of scales and that there is no obstacle to taking a continuum limit. This lends further support to the asymptotic safety scenario for gravity.
Highlights
Quantum gravity is one of the great outstanding problems of theoretical physics
We find that our lattice spacings are smaller than the Planck length and that for our finest lattice spacings we are starting to see a separation of scales, such that the lattice spacing is starting to become much smaller than the Planck scale
We find that restricting our sources to come from the largest three slice minimizes finite lattice spacing effects, and it is the same procedure that we have used in previous work on the spectral dimension [9] and for our studies of Kähler-Dirac fermions [30]
Summary
Quantum gravity is one of the great outstanding problems of theoretical physics. One possible approach to obtaining a consistent, predictive theory is the asymptotic safety scenario of Weinberg [1]. A study of fermion bilinear condensates provides strong evidence that this Uð1Þ symmetry is not spontaneously broken at order of the Planck scale, implying that fermion bound states do not acquire unacceptably large masses due to chiral symmetry breaking These results for Kähler-Dirac fermions in EDT are highly nontrivial and provide further evidence for the asymptotic safety scenario for gravity and matter. We find that our lattice spacings are smaller than the Planck length and that for our finest lattice spacings we are starting to see a separation of scales, such that the lattice spacing is starting to become much smaller than the Planck scale This provides evidence that does the formulation recover the correct long-distance physics, and that there is no barrier to taking the continuum limit. The Appendix gives some details of the fitter used in the analysis
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