= Ten-dimensional super Yang-Mills theory
{title2=$\mathcal N=1\text{ in }10D\longrightarrow\mathcal N=4\text{ in }4D$}
Minimal ten-dimensional <supersymmetric gauge theory> contains a <gauge field> and an adjoint <Majorana-Weyl spinor>. They have eight propagating <bosonic> and eight propagating <fermionic> states per gauge generator and sixteen real <supercharges>. A toroidal zero-mode <dimensional reduction> to four dimensions gives one <gauge field>, six real adjoint <scalar fields>, and four adjoint <Weyl spinors>: a <four-dimensional N=4 super Yang-Mills theory>. The internal field strength $F_{mn}=-ig[X_m,X_n]$ gives the nonnegative <scalar potential> $V=\frac{g^2}{4}\sum_{m,n}\lVert[X_m,X_n]\rVert^2$, where the norm uses a positive invariant inner product on the <Lie algebra>. Its minima are commuting tuples of adjoint <scalar fields>.
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