We give a systematic method to calculate higher derivative corrections to low-energy effective theories of solitons, which are in general nonlinear sigma models on the moduli spaces of the solitons. By applying it to the effective theory of a single BPS non-Abelian vortex in U(N) gauge theory with N fundamental Higgs fields, we obtain four-derivative corrections to the effective sigma model on the moduli space C×CP N-1. We compare them with the Nambu-Goto action and the Faddeev-Skyrme model. We also show that Yang- Mills instantons/monopoles trapped inside a non-Abelian vortex membrane/string are not modified in the presence of higher derivative terms.
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