Nonperturbative test of the Maldacena-Milekhin conjecture for the BMN matrix model

Abstract

We test a conjecture by Maldacena and Milekhin for the ungauged version of the Berenstein-Maldacena-Nastase (BMN) matrix model by lattice Monte Carlo simulation. The numerical results reproduce the perturbative and gravity results in the limit of large and small flux parameter, respectively, and are consistent with the conjecture.

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

“…In the limit µ → 0, the deformation terms vanish and one expects the above model to converge to the BFSS model. This, however, assumes that there is no phase transition between the models, and indeed evidence until now supports this assumption [5,19,22]. Note also that the singlet constraint (3.4) is not affected by the deformation.…”

“…[19] and we reproduce the correct scaling of the internal energy of the gravitational system at low temperatures, which is the strongly-coupled regime of this model. Concerning numerical simulations, the usefulness of this specific model arises because the flat direction is under better control and simulations become stable at lower temperatures [5,[20][21][22]. At the same time, a drawback is that the dual geometry is not known analytically.…”

“…In general, the γ I , I = 1, • • • , 10 matrices are 16 × 16 sub-matrices of the 32 × 32 ten-dimensional Gamma matrices Γ I . 6 For a more comprehensive analysis we refer to [5] and [22] for this potential and more discussions on the stability obtained in the simulations. 7 See ref.…”

“…The µ → 0 limit was studied in a different setting in ref. [22] and a quadratic extrapolation was used for observables such as E/N 2 and R 2 /N 2 , however, we are agnostic about odd or even preference of the µ extrapolations.…”

“…The linear extrapolations are only used to indicate, in accordance with figure8, that we see a negligible slope for E as well as to highlight the diverging behavior for µ < 0.5 that sets in at lower temperatures. The µ → 0 limit was studied in a different setting in ref [22]. and a quadratic extrapolation was used for observables such as E/N 2 and R 2 /N 2 , however, we are agnostic about odd or even preference of the µ extrapolations.…”