Maximally Supersymmetric RG Flows in 4D and Integrability

TL;DR

This paper studies a specific deformation of $ ext{N}=4$ Super Yang-Mills theory, exploring its classical action, integrability properties, and holographic aspects, with a focus on understanding how the deformation affects these features.

Contribution

It provides a closed-form classical action for the deformed theory on $S^3 imes ext{R}$ and investigates its integrability at two-loop order, highlighting potential preservation of integrability.

Findings

Classical action expressed in closed form for the deformed theory.

Two-loop analysis shows accidental symmetry enhancement, matching undeformed $ ext{N}=4$ SYM.

Indications that the deformation may preserve integrability, but not conclusively established.

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.