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

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.

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

Pini,

Vallarino

2024

Exact results for giant graviton four-point correlators

Brown,

Galvagno,

Wen

2024

We study the four-point correlator $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2\mathcal{DD}\right\rangle $$ O 2 O 2 DD in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory (SYM) with SU(N) gauge group, where $$ {\mathcal{O}}_2 $$ O 2 represents the superconformal primary operator with dimension two, while $$ \mathcal{D} $$ D denotes a determinant operator of dimension N, which is holographically dual to a giant graviton D3-brane extending along S5. We analyse the integrated correlator associated with this observable, obtained after integrating out the spacetime dependence over a supersymmetric invariant measure. Similarly to other classes of integrated correlators in $$ \mathcal{N} $$ N = 4 SYM, this integrated correlator can be computed through supersymmetric localisation on the four-sphere. Employing matrix-model recursive techniques, we demonstrate that the integrated correlator can be reformulated as an infinite sum of protected three-point functions with known coefficients. This insight allows us to circumvent the complexity associated with the dimension-N determinant operator, significantly streamlining the large-N expansion of the integrated correlator. In the planar limit and beyond, we derive exact results for the integrated correlator valid for all values of the ’t Hooft coupling, and investigate the resurgent properties of their strong coupling expansion. Additionally, in the large-N expansion with fixed (complexified) Yang-Mills coupling, we deduce the SL(2, ℤ) completion of these results in terms of the non-holomorphic Eisenstein series. The proposed modular functions are confirmed by explicit instanton calculations from the matrix model, and agree with expectations from the holographic dual picture of known results in type IIB string theory.

Large-N integrated correlators in $$ \mathcal{N} $$ = 4 SYM: when resurgence meets modularity

Dorigoni,

Treilis

2024

Exact expressions for certain integrated correlators of four half-BPS operators in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory with gauge group SU(N) have been recently obtained thanks to a beautiful interplay between supersymmetric localisation and modular invariance. The large-N expansion at fixed Yang-Mills coupling of such integrated correlators produces an asymptotic series of perturbative terms, holographically related to higher derivative interactions in the low energy expansion of the type IIB effective action, as well as exponentially suppressed corrections at large N, interpreted as contributions from coincident (p, q)-string world-sheet instantons. In this work we define a manifestly modular invariant Borel resummation of the perturbative large-N expansion of these integrated correlators, from which we extract the exact non-perturbative large-N sectors via resurgence analysis. Furthermore, we show that in the ’t Hooft limit such modular invariant non-perturbative completions reduce to known resurgent genus expansions. Finally, we clarify how the same non-perturbative data is encoded in the decomposition of the integrated correlators based on SL(2, ℤ) spectral theory.