  Supertubes are supersymmetric configurations in string theory in which branes
are extending along a closed curve. For a supertube of codimension two, its
dipole charge is characterized by the duality monodromy around the closed
curve. When multiple codimension-2 supertubes are present, the monodromies
around different supertubes can be non-commuting, namely non-Abelian.
Non-Abelian configurations of supertubes are expected to play an important role
in non-perturbative physics of string theory, especially black holes. In this
paper, in the framework of five-dimensional supergravity, we construct exact
solutions describing codimension-2 supertubes in three-dimensional space. We
use an extension formula to construct a three-dimensional solution from a
two-dimensional seed solution. The two-dimensional seed is an F-theory like
configuration in which a torus is nontrivially fibered over a complex plane. In
the first example, there is a stack of circular supertubes around which there
is a non-trivial monodromy. In some cases this can be thought of as a
microstate of a black hole in AdS_2 x S^2. The second example is an
axi-symmetric solution with two stacks of circular supertubes with non-Abelian
monodromies. In addition, there is a continuous distribution of charges on the
symmetry axis.
