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

Understand

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.