Non-planar data of $$ \mathcal{N} $$ = 4 SYM

179

143

We present the complete formula for the cusp anomalous dimension at four loops in QCD and in maximally supersymmetric Yang-Mills. In the latter theory it is given byOur approach is based on computing the correlation function of a rectangular light-like Wilson loop with a Lagrangian insertion, normalized by the expectation value of the Wilson loop. In maximally supersymmetric Yang-Mills theory, this ratio is a finite function of a cross-ratio and the coupling constant. We compute it to three loops, including the full colour dependence. Integrating over the position of the Lagrangian insertion gives the fourloop Wilson loop. We extract its leading divergence, which determines the four-loop cusp anomalous dimension. Finally, we employ a supersymmetric decomposition to derive the last missing ingredient in the corresponding QCD result.

Section: Discussionmentioning

confidence: 99%

Section: The Wilson Loop Integrand From a Correlation Functionmentioning

confidence: 99%

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The full four-loop cusp anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills and QCD

Henn

Korchemsky

Mistlberger

2020

179

143

“…For some previous non-planar studies of anomalous dimension and correlation functions, see e.g. [63,63,[120][121][122][123][124][125][126][127][128]. Second, the non-planar data would be useful for the study of possible hidden symmetries in the non-planar sector.…”

Section: Jhep04(2021)176mentioning

confidence: 99%

Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

Lin

Yang

2021

Form factors, as quantities involving both local operators and asymptotic particle states, contain information of both the spectrum of operators and the on-shell amplitudes. So far the studies of form factors have been mostly focused on the large Nc planar limit, with a few exceptions of Sudakov form factors. In this paper, we discuss the systematical construction of full color dependent form factors with generic local operators. We study the color decomposition for form factors and discuss the general strategy of using on-shell unitarity cut method. As concrete applications, we compute the full two-loop non-planar minimal form factors for both half-BPS operators and non-BPS operators in the SU(2) sector in $$ \mathcal{N} $$ N = 4 SYM. Another important aspect is to investigate the color-kinematics (CK) duality for form factors of high-length operators. Explicit CK dual representation is found for the two-loop half-BPS minimal form factors with arbitrary number of external legs. The full-color two-loop form factor result provides an independent check of the infrared dipole formula for two-loop n-point amplitudes. By extracting the UV divergences, we also reproduce the known non-planar SU(2) dilatation operator at two loops. As for the finite remainder function, interestingly, the non-planar part is found to contain a new maximally transcendental part beyond the known planar result.

“…While less is known about non-planar anomalous dimensions there are a number of impressive perturbative results for specific operators. For example, twist-two operators at four loops were studied using standard Feynman diagramatics [9,10] as well as twistor methods [11], and the four-loop non-planar correction to the cusp anomalous dimension was computed in [12]. Additionally, the Hexagon formalism for correlation functions, [13][14][15][16], provides an integrability-based method to studying non-planar N = 4 SYM.…”

Section: Introductionmentioning

confidence: 99%

One-loop non-planar anomalous dimensions in super Yang-Mills theory

McLoughlin

Pereira

Spiering

2020

Self Cite

We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.