  We study line operators in the two-dimensional sigma-model on PSl(n|n) using
the current-current OPEs. We regularize and renormalize these line operators,
and compute their fusion up to second order in perturbation theory. In
particular we show that the transfer matrix associated to a one-parameter
family of flat connections is free of divergences. Moreover this transfer
matrix satisfies the Hirota equation (which can be rewritten as a Y-system, or
Thermodynamic Bethe Ansatz equations) for all values of the two parameters
defining the sigma-model. This provides a first-principles derivation of the
Hirota equation which does not rely on the string hypothesis nor on the
assumption of quantum integrability.
