  We derive an effective Maxwell-London equation for entangled polymer complex
under the topological constraint, borrowing the theoretical framework from the
topological field theory. We find that the transverse current flux of the test
polymer chain, surrounded with entangled chains, decays exponentially from its
average position with finite penetration depth, which is analogous to the
magnetic-field decay in a superconductor (SC). Like as the mass acquirement of
photons in SC is the origin of the magnetic-field decay, the polymer earns
uncrossible intersections along the chain due to the preserved linking number,
which restricts the deviation of the transverse polymer current in the normal
direction. Interestingly, this picture is well incorporated with the most
successful phenomenological theory of the so called tube model, of which
researchers have long pursued its microscopic origin. The correspondence of our
equation of motion to the tube model claims that the confining tube potential
is a consequence of the topological constraint (linking number). The tube
radius is attributed to the decay length, and increasing the retracting force
at intersections or increasing the number of intersections (linking number),
the tube becomes narrow and tighter. It further shows that the probability of
the tube leakage decays exponentially with the decay length of tube radius.
