  I propose a way of unambiguously parallel transporting fields on non-Abelian
flux tubes, or strings, by means of two gauge fields. One gauge field
transports along the tube, while the other transports normal to the tube.
Ambiguity is removed by imposing an integrability condition on the pair of
fields. The construction leads to a gauge theory of mathematical objects known
as Lie 2-groups, which are known to result also from the parallel transport of
the flux tubes themselves. The integrability condition is also shown to be
equivalent to the assumption that parallel transport along nearby string
configurations are equal up to arbitrary gauge transformations. Attempts to
implement this condition in a field theory leads to effective actions for
two-form fields.
