Maximally supersymmetric RG flows in 4D and integrability

We revisit the leading irrelevant deformation of N = 4 Super Yang-Mills theory that preserves sixteen supercharges. We consider the deformed theory on S³× ℝ. We are able to write a closed form expression of the classical action thanks to a formalism that realizes eight supercharges off shell. We then investigate integrability of the spectral problem, by studying the spin-chain Hamiltonian in planar perturbation theory. While there are some structural indications that a suitably defined deformation might preserve integrability, we are unable to settle this question by our two-loop calculation; indeed up to this order we recover the integrable Hamiltonian of undeformed N = 4 SYM due to accidental symmetry enhancement. We also comment on the holographic interpretation of the theory.