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A bstract We consider a compactification of 4D N N = 4 SYM, with SU (N) gauge group, on a circle with anti-periodic boundary conditions for the fermions. We couple the theory to a constant background gauge field along the circle for an abelian subgroup of the R -symmetry which allows to preserve four supersymmetries. The 3D effective theory exhibits gapped and ungapped phases, which we argue are holographically dual, respectively, to a supersymmetric soliton in AdS 5 × S 5, and a particular quotient of AdS 5 × S 5. The gapped phase corresponds to an IR 3D N N = 2 supersymmetric Yang-Mills-Chern-Simons theory at level N, while the ungapped phase is naturally identified with the root of a Higgs branch in the 3D theory. We discuss the extension of the twisting procedure to maximally SUSY Yang-Mills theories in different dimensions, obtaining the relevant duals for 2D and 6D, and comment on the odd dimensional cases.
Kumar et al. (Mon,) studied this question.