%ACaetano, João%APeelaers, Wolfger%ARastelli, Leonardo%BJournal Name: Journal of High Energy Physics; Journal Volume: 2021; Journal Issue: 12 %D2021%I %JJournal Name: Journal of High Energy Physics; Journal Volume: 2021; Journal Issue: 12 %K %MOSTI ID: 10376825 %PMedium: X %TMaximally supersymmetric RG flows in 4D and integrability %XA bstract We revisit the leading irrelevant deformation of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory that preserves sixteen supercharges. We consider the deformed theory on S 3 × 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 $$ \mathcal{N} $$ N = 4 SYM due to accidental symmetry enhancement. We also comment on the holographic interpretation of the theory. %0Journal Article