Twisted circle compactification of $\mathcal{N}=4$ SYM and its Holographic Dual

TL;DR

This paper studies a twisted compactification of 4D $ ext{N}=4$ SYM on a circle, revealing dual phases with distinct holographic descriptions and extending the approach to other dimensions.

Contribution

It introduces a novel twisting method preserving supersymmetry in compactified $ ext{N}=4$ SYM and explores its holographic duals across various dimensions.

Findings

Identification of gapped and ungapped phases with specific holographic duals.

Connection of the gapped phase to a 3D supersymmetric Yang-Mills-Chern-Simons theory.

Extension of the twisting procedure to 2D and 6D maximally SUSY Yang-Mills theories.

Abstract

We consider a compactification of 4D $\mathcal{N}=4$ 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$_{5}\times S^{5}$, and a particular quotient of AdS$_5\times S^5$. The gapped phase corresponds to an IR 3D $\mathcal{N}=2$ 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.