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The realization of center and chiral symmetries in $\mathcal{N}=1$ superYang-Mills theory (SYM) is investigated on a four-dimensional Euclidean latticeby means of Monte Carlo methods. At zero temperature this theory is expected toconfine external fundamental charges and to have a non-vanishing gauginocondensate, which breaks the non-anomalous Z$_{2\textrm{N}_{c}}$ chiralsymmetry. In previous studies at finite temperatures, the phase transitionscorresponding to deconfinement and chiral restoration were observed to occur atroughly the same critical temperature for SU(2) gauge group. We find furtherevidences for this observation from new measurements at smaller latticespacings using the fermion gradient flow, and we discuss the agreement of ourfindings with conjectures from superstring theory. The implementation of thegradient flow technique allows us also to estimate, for the first time, thecondensate at zero temperatures and zero gaugino mass with Wilson fermions.

A study of center and chiral symmetry realization in thermal $\mathcal{N}=1$ super Yang-Mills theory using the gradient flow