TY - JOUR

T1 - Newtonian binding from lattice quantum gravity

AU - Dai, Mingwei

AU - Laiho, Jack

AU - Schiffer, Marc

AU - Unmuth-Yockey, Judah

N1 - Funding Information:
The authors thank Claude Bernard and Simon Catterall for valuable discussions, and we thank Simon Catterall and Fleur Versteegen for comments on the paper. The work of J. L. was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Award No. DE-SC0009998. The work of J. U.-Y. was supported by the U.S. Department of Energy Grant No. DE-SC0019139 and by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The work of M. S. was supported by the German Academic Scholarship Foundation and gratefully acknowledges hospitality at Syracuse University and at CP3-Origins, University of Southern Denmark, during various stages of this project. Computations were performed in part on the Syracuse University HTC Campus Grid and were supported by NSF Grant No. ACI-1341006. Computations for this work were also carried out in part on facilities of the USQCD Collaboration, which are funded by the Office of Science of the U.S. Department of Energy.
Publisher Copyright:
© 2021 authors. Published by the American Physical Society.

PY - 2021/6/1

Y1 - 2021/6/1

N2 - We study scalar fields propagating on Euclidean dynamical triangulations (EDTs). 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 nonrelativistic limit. We find a binding energy compatible with what one expects for the ground state energy by solving the Schrödinger equation for Newton's potential. Agreement with this expectation is obtained in the infinite-volume, continuum limit of the lattice calculation, providing nontrivial 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.

AB - We study scalar fields propagating on Euclidean dynamical triangulations (EDTs). 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 nonrelativistic limit. We find a binding energy compatible with what one expects for the ground state energy by solving the Schrödinger equation for Newton's potential. Agreement with this expectation is obtained in the infinite-volume, continuum limit of the lattice calculation, providing nontrivial 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.

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U2 - 10.1103/PhysRevD.103.114511

DO - 10.1103/PhysRevD.103.114511

M3 - Article

AN - SCOPUS:85108911886

SN - 2470-0010

VL - 103

JO - Physical Review D

JF - Physical Review D

IS - 11

M1 - 114511

ER -