Modular-invariant large-$N$ completion of an integrated correlator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory

Abstract

The use of supersymmetric localisation has recently led to modular covariant expressions for certain integrated correlators of half-BPS operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory with a general classical gauge group $G_N$. Here we determine generating functions that encode such integrated correlators for any classical gauge group and provide a proof of previous conjectured formulae. This gives a systematic understanding of the relation between properties of these correlators at finite $N$ and their expansions at large $N$. In particular, it determines a duality-invariant non-perturbative completion of the large-$N$ expansion in terms of a sum of novel non-holomorphic modular functions. These functions are exponentially suppressed at large $N$ and have the form of a sum of contributions from coincident $(p,q)$-string world-sheet instantons.

25 + 15 pages; v2: minor changes, version published in JHEP

References in corpus (9)

• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Exact properties of an integrated correlator in $\mathcal{N}=4$ $SU(N)$ SYM
• A novel representation of an integrated correlator in $\mathcal{N}=4$ SYM theory
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods
• The SAGEX Review on Scattering Amplitudes, Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their $\mathcal{N}=4$ supersymmetric Yang-Mills duals
• Large $N$ expansion of an integrated correlator in $\mathcal{N}=4$ SYM
• On topological recursion for Wilson loops in $\mathcal{N}=4$ SYM at strong coupling

Cited by in corpus (8)

• Generating functions and large-charge expansion of integrated correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Laplace-difference equation for integrated correlators of operators with general charges in $\mathcal{N}=4$ SYM
• Casimir Energy and Modularity in Higher-dimensional Conformal Field Theories
• The planar limit of integrated 4-point functions
• Integrated correlators at strong coupling in an orbifold of $\mathcal{N}=4$ SYM
• Integrated correlators with a Wilson line in a $\mathcal{N}=2$ quiver gauge theory at strong coupling
• Integrated correlators of coincident Wilson lines in $SU(N)$ gauge theories at strong coupling
• Matrix models for extremal and integrated correlators of higher rank