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Ward and Nielsen Identities for ABJM Theory in ${\cal N}=1$ Superspace

The structures and the associated gauge algebra of ABJM theory in ${\cal N}=1$ superspace are reviewed. We derive the Ward identities of the theory in the class of Lorentz-type gauges at quantum level to justify the renormalizability of the model. We compute the Nielsen identities for the two-point functions of the theory with the help of enlarged BRST transformation. The identities are derived in ABJM theory to ensure the gauge independence of the physical poles of the Green's functions.