Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2405.10204

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

Daniele Dorigoni·Rudolfs Treilis
View original source ↗Read source document ↗Export metadata ↓

Abstract

Exact expressions for certain integrated correlators of four half-BPS operators in $\mathcal{N}=4$ 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 $\rm{SL}(2,\mathbb{Z})$ spectral theory.

Explore related subjects

hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Daniele Dorigoni, Rudolfs Treilis. 2024-05-16. Large-$N$ integrated correlators in $\mathcal{N}=4$ SYM: when resurgence meets modularity. https://arxiv.org/abs/2405.10204

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fortuitous Chaos, BPS Black Holes, and Random Matrices

The ``fortuitous'' Bogomol'nyi-Prasad-Sommerfield (BPS) sector states in gauge theory have been argued to furnish a description, through holography, of generic BPS black hole microstates. They are expected to be strongly chaotic, a necessary feature to capture the black hole dynamics. This dovetails nicely with the existence of various random matrix models of JT supergravity with extended supersymmetry, within which the BPS chaos must be contained as a subsector. This paper identifies and studies a simple random matrix model that underlies all known random matrix models of JT supergravity. It is argued that it captures many essential universal features of fortuitous BPS chaos. The model is topological, naturally interpolating between the Bessel and Airy models, where the gap energy $E_0$ controls the interpolation, and seems to have a simple intersection theory interpretation.

hep-th↗
arXiv2026

Introduction to Generalized Symmetries

These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University. We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge theories, before introducing non-invertible symmetries in $(1+1)$-dimensional systems. The basic structure of fusion categories is then discussed, including a discussion of categorical analogs of discrete gauging and representation theory. We subsequently turn to $(3+1)$-dimensional theories, where several physical applications of non-invertible symmetries are discussed. These notes are intended to be largely self-contained, and require no prior familiarity with subjects such as conformal field theory or lattice models.

hep-th↗
arXiv2026

Planar loop integrands from cuts in $D$ dimensions

We present a direct reconstruction formula for planar loop integrands from $D$-dimensional generalized unitarity cuts in any colored theory. The reconstruction combinatorics is separated from the theory-dependent tree amplitudes entering the cuts: for the $L$-loop $n$-point color-ordered amplitude, the integrand is expressed as a sum over admissible non-scaleless scalar graphs dressed by corresponding cuts in $D$ dimensions; the coefficients are given by the universal Möbius-inversion formula of the refinement poset, or equivalently one minus the Euler characteristics of associated complexes. As an application we write down closed-formulas for loop integrands in pure Yang--Mills theory, where the required cuts are generated by gluing $D$-dimensional tree amplitudes and summing over internal gluon states. We also use the two-loop five-point case as a validation, comparing with known integrand data and after integration-by-parts reduction, with known integrated helicity amplitudes. The same framework also produces compact cut-organized data for larger examples, including the two-loop six-point and three-loop four-point cases. We also describe the corresponding simplification in maximally supersymmetric Yang--Mills theory, where the absence of bubble and triangle subgraphs reduces the relevant cut poset substantially.

hep-th↗