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The derivation of effective equations for group field theories is discussedfrom a variational point of view, with the action being determined by thefidelity of the trial state with respect to the exact state. It is shown howthe maximisation procedure with respect to the parameters of the trial statelead to the expected equations, in the case of simple condensates. Furthermore,we show that the second functional derivative of the fidelity gives a compactway to estimate, within the effective theory itself, the limits of itsvalidity. The generalisation can be extended to include the Nakajima--Zwanzigprojection method for general mixed trial states.

Effective equations for GFT condensates from fidelity