How to test the gauge/gravity duality with lattice simulations
Lattice field theories are a useful tool to define gauge theories in their non-perturbative regime. At the same time, the gauge/gravity duality conjectures that certain gauge theories in the non-perturbative regime are dual to weakly-coupled gravity. This suggests the possibility of relating weakly-coupled gravity to gauge theories defined on the lattice. As a first step, this conjecture needs to be tested by comparing suitable observables on both sides of the duality. If this first step is successful the duality could open the door to a non-perturbative definition of gravity via gauge theories defined on a lattice.
I will focus on the first lattice calculation of D0-branes quantum mechanics with a controlled continuum and large-N limit. A comparison of the internal energy in this dimensionally reduced supersymmetric gauge theory and its dual gravitational theory represents a decisive step towards precise numerical tests of the gauge/gravity conjecture.