  We study a junction of three quantum wires enclosing a magnetic flux. This is
the simplest problem of a quantum junction between Tomonaga-Luttinger liquids
in which Fermi statistics enter in a non-trivial way. We present a direct
connection between this problem and the dissipative Hofstadter problem, or
quantum Brownian motion in two dimensions in a periodic potential and an
external magnetic field, which in turn is connected to open string theory in a
background electromagnetic field. We find non-trivial fixed points
corresponding to a chiral conductance tensor leading to an asymmetric flow of
the current.
