= Massive two-form at closed-string level two
{title2=$M^2=8\pi T$}
Each level-two chiral sector of the critical <closed string> is the <symmetric traceless square> $S^2_0V$ of the massive <little group> vector space. The <tensor product> of its two sectors contains the <exterior square> $\Lambda^2V$: the equivariant map $(S,T)\mapsto ST-TS$ is onto the antisymmetric matrices. Compact-group complete reducibility realizes this quotient as a subrepresentation. It describes a <massive two-form field> with $M^2=8\pi T=4/\alpha'$.
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