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We disclose the mathematical structure underlying the gauge field sector ofthe recently constructed non-abelian superconformal models in six spacetimedimensions. This is a coupled system of 1-form, 2-form, and 3-form gaugefields. We show that the algebraic consistency constraints governing thissystem permit to define a Lie 3-algebra, generalizing the structural Liealgebra of a standard Yang-Mills theory to the setting of a higher bundle.Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-typeoperator Q, this higher bundle can be compactly described by means of aQ-bundle; its fiber is the shifted tangent of the Q-manifold corresponding tothe Lie 3-algebra and its base the odd tangent bundle of spacetime equippedwith the de Rham differential. The generalized Bianchi identities can then beretrieved concisely from Q^2=0, which encode all the essence of the structuralidentities. Gauge transformations are identified as vertical innerautomorphisms of such a bundle, their algebra being determined from a Q-derivedbracket.

Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions