SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling

TL;DR

This paper explores the algebraic structure and integrability properties of supersymmetric gauge theories with sixteen supercharges, analyzing their weak and strong coupling regimes through dimensional reduction, spin chain models, and string duals.

Contribution

It explicitly constructs the SU(2|2) algebra at strong coupling and constrains the spin chain and S-matrix structures at weak coupling, revealing signs of integrability.

Findings

Signs of integrability up to two-loop order in the three-dimensional theory.

Explicit construction of the SU(2|2) algebra at strong coupling.

Identification of the string dual as the IIA plane-wave geometry.

Abstract

We consider the dimensional reductions of N=4 Supersymmetric Yang-Mills theory on R x S^3 to the three-dimensional theory on R x S^2, the orbifolded theory on R x S^3/Z_k, and the plane-wave matrix model. With explicit emphasis on the three-dimensional theory, we demonstrate the realization of the SU(2|3) algebra in a radial Hamiltonian framework. Using this structure we constrain the form of the spin chains, their S-matrices, and the corresponding one- and two-loop Hamiltonian of the three dimensional theory and find putative signs of integrability up to the two-loop order. The string duals of these theories admit the IIA plane-wave geometry as their Penrose limit. Using known results for strings quantized on this background, we explicitly construct the strong-coupling dual extended SU(2|2) algebra and discuss its implications for the gauge theories.