Precision test of the gauge/gravity duality in two-dimensional N=(8,8) SYM

The $\epsilon - p$ is calculated from lattice simulations of two dimensional ${\cal N}=(8,8)$ $SU(N)$ SYM to test the gauge gravity duality. We employ the Sugino action with keeping two of sixteen supercharges exactly on the lattice. The thermodynamics of this gauge theory is described by the black 1-branes at low temperature. The internal energy density $\epsilon$ and the pressure $p$ can be analytically estimated in the gravitational theory. The lattice results in $N=12$ show that $\epsilon - p$ of the thermal SYM reproduces the prediction of the gravitational theory for the dimensionless temperature $T_{\rm eff}<0.4$. This clearly indicates that the duality is valid in this system.