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

Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation