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

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>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 <jats:italic>N</jats:italic> 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 <jats:italic>N</jats:italic> than in the BFSS matrix model are possible. Hence, we can perform a precision measurement of the large <jats:italic>N</jats:italic> continuum energy at the lowest temperatures to date. The energy is in perfect agreement with supergravity predictions including estimations of <jats:italic>α</jats:italic>′-corrections from previous simulations. At the lowest temperature where we can simulate efficiently (<jats:italic>T</jats:italic> = 0<jats:italic>.</jats:italic>25<jats:italic>λ</jats:italic><jats:sup>1<jats:italic>/</jats:italic>3</jats:sup>, where <jats:italic>λ</jats:italic> 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<jats:italic>/N</jats:italic><jats:sup>4</jats:sup> corrections at a fixed temperature with good accuracy, which was previously unknown.</jats:p>