Maximally Supersymmetric RG Flows in 4D and Integrability

Abstract

We revisit the leading irrelevant deformation of $\mathcal{N}=4$ Super Yang-Mills theory that preserves sixteen supercharges. We consider the deformed theory on $S^3\times \mathbb{R}$. 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 $\mathcal{N}=4$ SYM due to accidental symmetry enhancement. We also comment on the holographic interpretation of the theory.

arXiv comment39 pages; v2: references and comments added

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• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Infinite pseudo-conformal symmetries of classical $T\bar{T}$, $J\bar{T}$ and $J{T}_a$ - deformed CFTs
• $T\bar{T}$ flow as characteristic flows
• $J\bar{T}$-deformed CFTs as non-local CFTs
• On Current-Squared Flows and ModMax Theories