Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods

Abstract

We study perturbative aspects of recently proposed integrated four-point correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills with all classical gauge groups using standard Feynman diagram computations. We argue that perturbative contributions of the integrated correlators are given by linear combinations of periods of certain conformal Feynman graphs, which were originally introduced for the construction of perturbative loop integrands of the un-integrated correlator. This observation allows us to evaluate the integrated correlators to high loop orders. We explicitly compute one of the integrated correlators up to four loops in the planar limit, and up to three loops for the other integrated correlator, and find agreement with the results obtained from supersymmetric localisation. The identification between the integrated correlators and certain periods also implies non-trivial relations among these periods, given that one may compute the integrated correlators using localisation. We illustrate this idea by considering one of the integrated correlators at five loops in the planar limit, where the localisation result leads to a prediction for the period of a certain six-loop integral.

arXiv commenttypos corrected, JHEP published version

References in corpus (37)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Superconformal Ward Identities and their Solution
• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT
• Three-Loop Four-Point Correlator in N=4 SYM
• Anomalous dimensions in N=4 SYM theory at order g^4
• Numbers and Functions in Quantum Field Theory
• Leading singularities and off-shell conformal integrals
• On the periods of some Feynman integrals
• Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
• Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM
• Knots and Numbers in ${\varphi }^4$ Theory to 7 Loops and Beyond
• Four-point functions in N=4 supersymmetric Yang-Mills theory at two loops
• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
• Simplifications of four-point functions in N=4 supersymmetric Yang-Mills theory at two loops
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• A note on four-point functions of conformal operators in N=4 Super-Yang Mills
• Modular Invariance in Superstring Theory From $\mathcal{N}=4$ Super-Yang-Mills
• Exact properties of an integrated correlator in $\mathcal{N}=4$ $SU(N)$ SYM
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• The Galois coaction on ${\varphi }^4$ periods
• Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality
• All three-loop four-point correlators of half-BPS operators in planar N=4 SYM
• Ten dimensional symmetry of N=4 SYM correlators
• A novel representation of an integrated correlator in $\mathcal{N}=4$ SYM theory
• Maximal $U(1{)}_Y$-violating $n$-point correlators in $\mathcal{N}=4$ super-Yang-Mills theory
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• All five-loop planar four-point functions of half-BPS operators in $\mathcal{N}=4$ SYM
• Maximal R-symmetry violating amplitudes in type IIB superstring theory
• Modular Forms and $SL(2,\mathbb{Z})$-covariance of type IIB superstring theory
• Non-planar data of $\mathcal{N}=4$ SYM
• Glue-and-Cut at Five Loops
• S-duality and the prepotential in N=2* theories (II): the non-simply laced algebras
• S-duality and the prepotential in N=2* theories (I): the ADE algebras
• Resumming instantons in N=2* theories with arbitrary gauge groups

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• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• Integrated correlators with a Wilson line in a $\mathcal{N}=2$ quiver gauge theory at strong coupling
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