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[en] We apply field theory methods to chains in the symmetric representation, with p boxes in the Young tableau, mapping them into a flag manifold nonlinear σ-model with a topological angle . Generalizing the Haldane conjecture, we argue that the models are gapped for but gapless for (for integer m), corresponding to a massless phase of the σ-model at . We confirm this with Monte Carlo calculations on the σ-model.