Monte Carlo Studies of Supersymmetric Matrix Quantum Mechanics with Sixteen Supercharges at Finite Temperature

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality.

Figure 1

The absolute value of the Polyakov line is plotted against $T$. The dashed line represents the result obtained by HTE up to the next leading order for $N=12$ [25]. The dotted line represents a fit to Eq. (4) with $a=0.15$ and $b=0.072$.

Figure 2

The internal energy is plotted against $T$. The dashed line represents the result obtained by HTE up to the next leading order for $N=12$ [25]. The solid line represents the asymptotic behavior at small $T$ predicted by the gauge-gravity duality based on the results obtained from dual black-hole geometry. The upper left panel magnifies the region, where the power-law behavior seems to set in.