22757 2306.00929 10.1007/JHEP02(2024)047 47 47 Large charge ’t Hooft limit of N $$ \mathcal{N} $$ = 4 super-Yang-Mills Regular Article - Theoretical Physics 1 94 2024 2 8 2023 8 10 2024 1 27 2024 2 8 The Author(s) 2024 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2024 2024 2 2 João Caetano joao.caetanus@gmail.com Shota Komatsu shota.komadze@gmail.com Yifan Wang yw6417@nyu.edu grid.9132.9 0000 0001 2156 142X Department of Theoretical Physics CERN 1211 Meyrin Switzerland https://ror.org/0190ak572 grid.137628.9 0000 0004 1936 8753 Center for Cosmology and Particle Physics New York University New York NY 10003 USA Abstract The planar integrability of N $$ \mathcal{N} $$ = 4 super-Yang-Mills (SYM) is the cornerstone for numerous exact observables. We show that the large charge sector of the SU(2) N $$ \mathcal{N} $$ = 4 SYM provides another interesting solvable corner which exhibits striking similarities despite being far from the planar limit. We study non-BPS operators obtained by small deformations of half-BPS operators with R-charge J in the limit J → ∞ with λ J ≡ g YM 2 J / 2 $$ {\lambda}_J\equiv {g}_{\textrm{YM}}^2J/2 $$ fixed. The dynamics in this large charge ’t Hooft limit is constrained by a centrally-extended psu $$ \mathfrak{psu} $$ (2|2)2 symmetry that played a crucial role for the planar integrability. To the leading order in 1/J, the spectrum is fully fixed by this symmetry, manifesting the magnon dispersion relation familiar from the planar limit, while it is constrained up to a few constants at the next order. We also determine the structure constant of two large charge operators and the Konishi operator, revealing a rich structure interpolating between the perturbative series at weak coupling and the worldline instantons at strong coupling. In addition we compute heavy-heavy-light-light (HHLL) four-point functions of half-BPS operators in terms of resummed conformal integrals and recast them into an integral form reminiscent of the hexagon formalism in the planar limit. For general SU(N) gauge groups, we study integrated HHLL correlators by supersymmetric localization and identify a dual matrix model of size J/2 that reproduces our large charge result at N = 2. Finally we discuss a relation to the physics on the Coulomb branch and explain how the dilaton Ward identity emerges from a limit of the conformal block expansion. We comment on generalizations including the large spin ’t Hooft limit, the combined large N-large J limits, and applications to general N $$ \mathcal{N} $$ = 2 superconformal field theories. Keywords Extended Supersymmetry Supersymmetric Gauge Theory ArXiv ePrint: 2306.00929