Title: SU(2) Pfaffian systems and gauge theory,
Abstract: Motivated by the description of Nurowski's conformal structure for maximally
symmetric homogeneous examples of bracket-generating rank 2 distributions in
dimension 5, aka $(2,3,5)$-distributions, we consider a rank $3$ Pfaffian
system in dimension 5 with $SU(2)$ symmetry. We find the conditions for which
this Pfaffian system has the maximal symmetry group (in the real case this is
the split real form of $G_2$), and give the associated Nurowski's conformal
classes. We also present a $SU(2)$ gauge-theoretic interpretation of the
results obtained.