Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice

We perform lattice simulations of two-dimensional supersymmetric Yang-Mills theory with sixteen supercharges with a lattice action which has two exact supercharges (Sugino lattice action). According to the gauge/gravity duality, the theory at finite temperature is expected to be well described by the corresponding black 1-branes, at low temperature in the large N limit. We aim to confirm the duality conjecture by comparing the lattice results with the theoretical predictions obtained in the gravity side. In this article, at the beginning of this study, we examine the supersymmetric Ward-Takahashi identity to test whether the lattice action reproduces the correct continuum theory. Numerical results of the SUSY WTI strongly suggest us that any cut-off effects, which break supersymmetry, disappear in the continuum limit. In addition, we study the issue of degenerate vacua and find that the admissiblilty condition or any other constraints of the link fields which guarantee the unique vacuum are not always needed.