We consider Yang-Mills theory with N = 1 super-translation group in eleven auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold Σ3 × S1, where Σ3 is a three-dimensional Lorentzian manifold and S1 is a circle. We show that in the infrared limit, when the metric on S1 is scaled down, the Yang-Mills action supplemented by a Wess-Zumino-type term reduces to the action of an M2-brane.
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The direct product structure is not necessary for the application of the adiabatic method. In general, it is enough if there is a fibration Z → X or if X is a calibrated submanifold of Z.
In the physics literature this limit is called infrared or low-energy limit (see e.g., Refs. 12–14).
In fact, in Refs. 12–14 the authors considered and super-Yang-Mills theories but the restriction to the pure Yang-Mills subsector does not change the picture.
