= Hermitian commutator potential in D-brane Yang-Mills theory
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{title2=$V=-\frac{1}{4g_{\mathrm{YM}}^2}\sum_{I,J}\operatorname{Tr}[\phi^I,\phi^J]^2\geq0$}
For Hermitian scalar matrices, their commutator is anti-Hermitian, so $-\operatorname{Tr}[\phi^I,\phi^J]^2=\operatorname{Tr}[\phi^I,\phi^J]^\dagger[\phi^I,\phi^J]\geq0$. Dimensional reduction gives $F_{IJ}=i[\phi^I,\phi^J]$, fixing the minus sign before the literal commutator square inside the conventional overall-negative Yang-Mills action. Commuting scalar expectation values minimize this potential and describe ordinary separated branes. A plus sign instead requires interpreting the squared symbol as the positive Hermitian norm, not literal matrix multiplication.
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