Twisted circle compactification of $$ \mathcal{N} $$ = 4 SYM and its holographic dual

Abstract

We consider a compactification of 4D $$ \mathcal{N} $$ 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 AdS5 × S5, and a particular quotient of AdS5 × S5. The gapped phase corresponds to an IR 3D $$ \mathcal{N} $$ 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.