A new super-exceptional embedding construction of the heterotic M5-branes sigma-model was recently shown to produce, at leading order in the super-exceptional vielbein components, the super-Nambu-Goto (Green-Schwarz-type) Lagrangian for the embedding fields plus the Perry-Schwarz Lagrangian for the free abelian self-dual higher gauge field. Beyond that, further fields and interactions emerge in the model, arising from probe M2- and probe M5-brane wrapping modes. Here we classify the full super-exceptional field content and work out some of its characteristic interactions from the rich super-exceptional Lagrangian of the model. We show that SU(2)xU(1)-valued scalar and vector fields emerge from probe M2- and M5-branes wrapping the vanishing cycle in the A_1-type singularity; together with a pair of spinor fields of U(1)-hypercharge +-1 and each transforming as SU(2) iso-doublets. Then we highlight the appearance of a WZW-type term in the super-exceptional PS-Lagrangian and find that on the electromagnetic field it gives the first-order non-linear DBI-correction, while on the iso-vector scalar field it has the form characteristic of the coupling of vector mesons to pions via the Skyrme baryon current. We discuss how this is suggestive of a form of SU(2)-flavor chiral hadrodynamics emerging on the single (N=1) M5 brane, different from, but akin to, holographic large-$N$ QCD.
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