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In this paper, we extend the Gribov-Zwanziger framework accounting for theexistence of Gribov copies to the mass deformed Bagger--Lambert--Gustavsson(BLG) theory in $\mathcal{N} =1 $ superspace. The restriction of the domain ofintegration in the Euclidean functional integral to the first Gribov horizon isimplemented, by adding a non-local horizon term to the effective action.Furthermore, the soft breaking of the BRST symmetry due to horizon term isrestored with the help of external sources. We compute the various Wardidentities for this theory relying on the Lie 3-algebras.

A mass-deformed BLG theory in Gribov-Zwanziger framework