Precision test of gauge/gravity duality in D0-brane matrix model at low temperature

Abstract

We test the gauge/gravity duality between the matrix model and type IIA string theory at low temperatures with unprecedented accuracy. To this end, we perform lattice Monte Carlo simulations of the Berenstein-Maldacena-Nastase (BMN) matrix model, which is the one-parameter deformation of the Banks-Fischler-Shenker-Susskind (BFSS) matrix model, taking both the large $N$ and continuum limits. We leverage the fact that sufficiently small flux parameters in the BMN matrix model have a negligible impact on the energy of the system while stabilizing the flat directions so that simulations at smaller $N$ than in the BFSS matrix model are possible. Hence, we can perform a precision measurement of the large $N$ continuum energy at the lowest temperatures to date. The energy is in perfect agreement with supergravity predictions including estimations of $\alpha'$-corrections from previous simulations. At the lowest temperature where we can simulate efficiently ($T=0.25\lambda^{1/3}$, where $\lambda$ is the 't Hooft coupling), the difference in energy to the pure supergravity prediction is less than $10\%$. Furthermore, we can extract the coefficient of the $1/N^4$ corrections at a fixed temperature with good accuracy, which was previously unknown.