# Schreiber Super-exceptional M5-brane model -- Emergence of SU(2)-flavor sector

An article that we have written:

• Super-exceptional M5-brane model:

Emergence of $SU(2)$-flavor sector

Journal of Geometry and Physics

Volume 170, December 2021, 104349

Abstract. A new super-exceptional embedding construction of the heterotic M5-brane's 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 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 their characteristic interactions from the rich super-exceptional Lagrangian of the model. We show that $\mathrm{SU}(2) \times U(1)$-valued scalar and vector fields emerge in the model from probe M2- and M5-branes wrapping the vanishing cycle in the $\mathrm{A}_1$-type singularity; together with a pair of spinor fields of $U(1)$-hypercharge $\pm 1$ 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 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 ($N=1$) heterotic M5-brane, different from, but akin to, large-N holographic QCD.

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