The planar limit of integrated 4-point functions

In a $$ \mathcal{N} $$ N = 2 superconformal gauge theory with matter hypermultiplets transforming in the symmetric and anti-symmetric representations of SU(N), we study the integrated correlators of two Coulomb-branch operators and two moment-map operators using localization. In the corresponding matrix model we identify the operator associated with the integrated insertions of moment-map operators and provide for it an exact expression valid for all values of the coupling constant in the planar limit. This allows us to study the integrated correlators at strong-coupling where we show that they behave as the 2-point functions of the Coulomb-branch operators, up to an overall constant dependent only on the conformal dimensions of the latter. The strong-coupling relation between integrated correlators and 2-point functions turns out to be the same as in $$ \mathcal{N} $$ N = 4 SYM at large N, despite the reduced amount of supersymmetry in our theory.

A matrix-model approach to integrated correlators in a $$ \mathcal{N} $$ = 2 SYM theory

Billò,

Frau,

Lerda

et al. 2024

Large charge ’t Hooft limit of $$ \mathcal{N} $$ = 4 super-Yang-Mills

Caetano,

Komatsu,

Wang

2024

The planar integrability of $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) is the cornerstone for numerous exact observables. We show that the large charge sector of the SU(2) $$ \mathcal{N} $$ 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 $$ {\lambda}_J\equiv {g}_{\textrm{YM}}^2J/2 $$ λ J ≡ g YM 2 J / 2 fixed. The dynamics in this large charge ’t Hooft limit is constrained by a centrally-extended $$ \mathfrak{psu} $$ 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 $$ \mathcal{N} $$ N = 2 superconformal field theories.

Integrated correlators at strong coupling in an orbifold of $$ \mathcal{N} $$ = 4 SYM

Pini,

Vallarino

2024

We consider the 4d$$ \mathcal{N} $$ N = 2 superconformal quiver gauge theory obtained by a ℤ2 orbifold of $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM). By exploiting supersymmetric localization, we study the integrated correlator of two Coulomb branch and two moment map operators and the integrated correlator of four moment map operators, determining exact expressions valid for any value of the ’t Hooft coupling in the planar limit. Additionally, for the second correlator, we obtain an exact expression also for the next-to-planar contribution. Then, we derive the leading terms of their strong-coupling expansions and outline the differences with respect to the $$ \mathcal{N} $$ N = 4 SYM theory.