Five-dimensional super Yang-Mills theory from ABJM theory

We derive five-dimensional super Yang-Mills theory from mass-deformed ABJM theory by expanding about $S^2$ for large Chern-Simons level $K$. We obtain the Yang-Mills coupling constant $g_{YM}^2 = 4π^2 R/K$. If we consider $S^3/{\mb{Z}_K}$ as a fiber bundle over $S^2$ then $R/K$ is the circumference of the fiber. The value on the coupling constant agrees with what one gets by compactifying M five-brane on that fiber. For this computation we take $R,K\to \infty$ while keeping $R/K$ at a fixed finite value. We also study mass deformed star-three-product BLG theory at K=1 and $R\to \infty$. In that limit we obtain Lorentz covariant supersymmetry variations and gauge variations of a non-Abelian tensor multiplet.

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