  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.
