Higher-derivative gauge interactions of Bagger-Lambert-Gustavsson theory in N=1 superspace

We study the structure of the gauge sector of the Bagger-Lambert-Gustavsson theory in the form proposed by van Raamsdonk, adapted to three dimensions, N=1 superspace. By using the novel Higgs mechanism proposed by Mukhi and Papageorgakis, we derive the manifestly N=1 supersymmetric higher-order terms (beyond the supersymmetric Yang-Mills action) that follow from the Bagger-Lambert-Gustavsson theory in its expansion with respect to the inverse gauge coupling constant squared. We find that all those terms have at least one anticommutator of the super-Yang-Mills field strength superfields as a factor, and thus are reducible to the supersymmetric Yang-Mills terms with the higher (spacetime) derivatives.