  Complexity of quantum phases of matter is often understood by the underlying
gauge structures, as was recognized by the $\mathbb{Z}_2$ and U(1) gauge theory
description of spin liquid in frustrated magnets. Anomalous Hall effect of
conducting electrons can intrisically arise from U(1) gauges expressing the
spatial modulation of ferromagnetic moments or from SU(2) gauges representing
the spin-orbit coupling effect. Similarly, in insulating ferro and
antiferromagnets, the magnon excitations can contribute to anomalous transports
by feeling the U(1) and SU(2) gauges arising from the features of ordered
moments or interactions. In this work, we report the emergent higher rank SU(3)
gauge structure in the magnon transport based on the thermal conductivity
measurements of MnSc$_2$S$_4$ in an applied field up to 14\,T. The thermal Hall
coefficient takes a substantial value when the material enters a
three-sublattice antiferromagnetic skyrmion phase, which is confirmed by the
large-scale spin wave theory. The excited magnons are dressed with SU(3) gauge
field, which is a mixture of three species of U(1) gauge fields originating
from the slowly varying magnetic moments on these sublattices.
