String Theory Journal Club

N=4 super-Yang-Mills (SYM) in four dimensions is integrable in the planar limit, allowing exact computations for a variety of observables. I will demonstrate that the large charge sector of N = 4 SYM with the SU(2) gauge group provides another interesting solvable corner, which is far from the planar limit but nevertheless exhibits similar structures. We study non-BPS operators obtained by small deformations of half-BPS operators with R-charge J in the double-scaling limit with J → ∞ and λ_J ≡ g^2 J/2 fixed. I will show thatthe spectrum and correlation functions in this large charge 't Hooft limit are constrained by the centrally-extended SU(2|2)^2 symmetry that played a crucial role in integrability in the planar limit. I will also show exact results in the large charge 't Hooft limit for certain three and four point functions. In the case of four point functions, I will be able to study integrated correlators for arbitrary SU(N) gauge groups by recasting results from supersymmetric localization to an 'emergent' matrix model of size J/2, and matchingit against the large charge analysis.