Five-loop Konishi in N=4 SYM

Abstract

We present a new method for computing the Konishi anomalous dimension in N=4 SYM at weak coupling. It does not rely on the conventional Feynman diagram technique and is not restricted to the planar limit. It is based on the OPE analysis of the four-point correlation function of stress-tensor multiplets, which has been recently constructed up to six loops. The Konishi operator gives the leading contribution to the singlet SU(4) channel of this OPE. Its anomalous dimension is the coefficient of the leading single logarithmic singularity of the logarithm of the correlation function in the double short-distance limit, in which the operator positions coincide pairwise. We regularize the logarithm of the correlation function in this singular limit by a version of dimensional regularization. At any loop level, the resulting singularity is a simple pole whose residue is determined by a finite two-point integral with one loop less. This drastically simplifies the five-loop calculation of the Konishi anomalous dimension by reducing it to a set of known four-loop two-point integrals and two unknown integrals which we evaluate analytically. We obtain an analytic result at five loops in the planar limit and observe perfect agreement with the prediction based on integrability in AdS/CFT.

42 pages, 7 figures; v2: reference added, minor corrections

References in corpus (8)

• Algorithm FIRE -- Feynman Integral REduction
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Wrapping at four loops in N=4 SYM
• Geometric approach to asymptotic expansion of Feynman integrals
• Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM
• Anomalous dimension with wrapping at four loops in N=4 SYM
• Konishi operator at intermediate coupling

Cited by in corpus (41)

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• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
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• Integrability of the AdS_5 x S^5 superstring and its deformations
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• Multiple zeta functions and double wrapping in planar N=4 SYM
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• Introduction to the thermodynamic Bethe ansatz
• The Quantum Deformed Mirror TBA II
• Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations
• Resummation and S-duality in N=4 SYM
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
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• Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM
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• Extracting OPE coefficient of Konishi at four loops
• Perturbative correlation functions of null Wilson loops and local operators
• Scaling dimensions from the mirror TBA
• Exceptional Operators in N=4 super Yang-Mills
• Cross-Order Integral Relations from Maximal Cuts
• "Short" spinning strings and structure of quantum AdS_5 x S^5 spectrum
• Integrable strings for AdS/CFT
• Static Gauge and Energy Spectrum of Single-mode Strings in AdS_5xS^5
• Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4 SYM
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• Towards QCD running in 5 loops: quark mass anomalous dimension
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• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
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