  We calculate the gaugino condensate in $SU(2)$ super Yang-Mills theory on an
asymmetric four-torus $\mathbb T^4$ with 't Hooft's twisted boundary
conditions. The $\mathbb T^4$ asymmetry is controlled by a dimensionless
detuning parameter $\Delta$, proportional to $L_3 L_4 - L_1 L_2$, with $L_i$
denoting the $\mathbb T^4$ periods. We perform our calculations via a path
integral on a $\mathbb T^4$. Its size is taken much smaller than the inverse
strong scale $\Lambda$ and the theory is well inside the semi-classical
weak-coupling regime. The instanton background, constructed for $\Delta\ll 1$
in arXiv:hep-th/0007113, has fractional topological charge $Q=\frac{1}{2}$ and
supports two gaugino zero modes, yielding a non-vanishing bilinear condensate,
which we find to be $\Delta$-independent. Further, the theory has a mixed
discrete chiral/$1$-form center anomaly leading to double degeneracy of the
energy eigenstates on any size torus with 't Hooft twists. In particular, there
are two vacua, $|0\rangle$ and $|1\rangle$, that are exchanged under chiral
transformation. Using this information, the $\Delta$-independence of the
condensate, and assuming further that the semi-classical theory is continuously
connected to the strongly-coupled large-$\mathbb T^4$ regime, we determine the
numerical coefficient of the gaugino condensate: $\langle 0|
\mbox{tr}\lambda\lambda|0\rangle=|\langle 1|
\mbox{tr}\lambda\lambda|1\rangle|=32\pi^2 \Lambda^3$, a result equal to twice
the known $\mathbb R^4$ value. We discuss possible loopholes in the continuity
approach that may lead to this discrepancy.
