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The two-dimensional supersymmetric Yang-Mills (SYM) theory with sixteensupercharges at large $N$ and strong 't~Hooft coupling is conjectured to bedual to certain supergravity solutions in the decoupling limit. We discretizethe gauge theory preserving a subset of supersymmetries on the lattice. Basedon the choice of a point in the moduli space for the expansion of the gaugelinks to target the correct continuum theory, one ends up with differentlattice geometries. In our previous work, we explored the free energy and thephase structure on a skewed torus corresponding to $A_{2}^{*}$ latticegeometry. Here, we will consider square lattice and calculate the free energy,equation of state and speed of sound in this strongly coupled supersymmetricplasma. Since there is no shear viscosity in two dimensions, we comment on theexpectations for the bulk viscosity from the calculations on the dualsupergravity side, which unlike the conformal $\mathcal{N}=4$ SYM case does notvanish and is proportional to the trace of energy-momentum tensor.

The properties of $D1$-branes from lattice super Yang--Mills theory using gauge/gravity duality