  We study the stability of the glassy equilibrium state of a directed polymer
in random media against weak perturbations including the intriguing problem of
temperature-chaos. The statistical correlation of two real replica systems
under perturbations, such as small difference of temperature, is studied using
the mapping to a quantum problem of interacting bosons. Explicit replica
symmetry breaking takes place being induced by the infinitesimally weak
perturbations in the $n \to 0$ limit followed by the thermodynamic limit which
leads to complete decorrelation of the two real replicas. The overlap lengths
anticipated by phenomenological scaling arguments are retrieved as a
correlation length associated with this explicit replica symmetry breaking.
