Advances in Theoretical and Mathematical Physics

Volume 27 (2023)

Number 1

Holographic space-time, Newton’s law, and the dynamics of horizons

Pages: 65 – 86



Tom Banks (Department of Physics and NHETC, Rutgers University, Piscataway, New Jersey, U.S.A.)

Willy Fischler (Department of Physics and Texas Cosmology Center, University of Texas, Austin, Tx., U.S.A.)


We revisit the construction of models of quantum gravity in $d$ dimensional Minkowski space in terms of random tensor models, and correct some mistakes in our previous treatment of the subject. We find a large class of models in which the large impact parameter scattering scales with energy and impact parameter like Newton’s law. The scattering amplitudes in these models describe scattering of jets of particles, and also include amplitudes for the production of highly meta-stable states with all the parametric properties of black holes. These models have emergent energy, momentum and angular conservation laws, despite being based on time dependent Hamiltonians. The scattering amplitudes in which no intermediate black holes are produced have a time-ordered Feynman diagram space-time structure: local interaction vertices connected by propagation of free particles (really Sterman–Weinberg jets of particles). However, there are also amplitudes where jets collide to form large meta-stable objects, with all the scaling properties of black holes: energy, entropy and temperature, as well as the characteristic time scale for the decay of perturbations. We generalize the conjecture of Sekino and Susskind, to claim that all of these models are fast scramblers. The rationale for this claim is that the interactions are invariant under fuzzy subgroups of the group of volume preserving diffeomorphisms, so that they are highly non-local on the holographic screen. We review how this formalism resolves the Firewall Paradox.

The work of W. Fischler is supported by the National Science Foundation under Grant Number PHY-1914679. The work of T. Banks is partially supported by the U.S. Dept. of Energy under grant DE-SC0010008.

Published 13 July 2023