Book/Dissertation / PhD Thesis

PUBDB-2026-02059

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Higher-Point Correlation Functions in N=4 Supersymmetric Yang­–Mills Theory

Bekov, A. (Corresponding author)DESY* ; Bargheer, T. (Thesis advisor)DESY*

2026
Verlag Deutsches Elektronen-Synchrotron DESY Hamburg

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Please use a persistent id in citations: doi:10.3204/PUBDB-2026-02059

Report No.: DESY-THESIS-2026-010

Abstract: This thesis investigates loop integrands of correlation functions of scalar half-BPS operators in four-dimensional $\mathcal{N}=4$ supersymmetric Yang–Mills (SYM) theory. $\mathcal{N}=4$ SYM provides a central “theoretical laboratory” due to its high degree of symmetry, its role in the AdS/CFT correspondence, and the emergence of integrability in the planar limit.First, we study planar higher-point generating functions, which combine infinitely many fixed-charge correlators into unified expressions using ten-dimensional coordinates that merge spacetime and R-symmetry variables. We compute the five-point generating function at one and two loops, and the six-point function at one loop. The results exhibit a recursive nesting structure in which higher-order ten-dimensional poles are controlled by lower-point correlators.Second, we analyze ten-dimensional null polygons, obtained as a specific kinematic limit of the generating functions, where these factorize into simpler polygon functions with disc topology. We present a twistor-based direct computation of the polygon integrands, and determine the two-loop integrands for any number of external operators. By imposing soft and collinear bootstrap constraints in off-shell kinematics, we uniquely fix the five-point pentagon integrand up to five loops. This provides a useful setting for testing dualities between correlation functions and massive scattering amplitudes.Finally, we go beyond the planar limit and compute the full non-planar five-loop four-point integrand for the lightest scalar operators. This is achieved using a GPU-accelerated algorithm for evaluating Grassmann multiplications in the twistor Feynman rules. The result shows that the integrand can be expressed purely in terms of genus-one contributions. Furthermore, it allows us to extract the non-planar five-loop correction to the Konishi anomalous dimension.These results provide new insight into the structure of higher-point correlation functions in $\mathcal{N}=4$ SYM and open avenues for further investigations of both planar and non-planar dynamics.

Note: Dissertation, Universität Hamurg, 2026

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. DFG project G:(GEPRIS)460391856 - Feldtheorie lösen mittels Integrabilität (460391856) (460391856)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2026

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Database coverage:

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