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Starting with the N=8 supersymmetric Yang-Mills theory on D2-branes and incorporating higher-derivative corrections to lowest nontrivial order, we perform a duality to derive the Lorentzian 3-algebra theory along with a set of derivative corrections. We find that these corrections can be expressed entirely in terms of intrinsic 3-algebra quantities: the 3-bracket and covariant derivatives. Our analysis is performed for both bosonic and fermionic terms. We conjecture that the derivative corrections we obtain are relevant for Euclidean 3-algebra theories as well.
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