Super-exceptional embedding construction of the heterotic M5: Emergence of SU(2)-flavor sector

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