Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM

By B. Eden, P. Heslop, G. Korchemsky, E. Sokatchev. 2012

148 citations recorded by the source corpus.

We present a construction of the integrand of the correlation function of four stress-tensor multiplets in N = 4 SYM at weak coupling. It does not rely on Feynman diagrams and makes use of the recently discovered symmetry of the integrand under permutations of external and integration points. This symmetry holds for any gauge group, so it can be used to predict the integrand both in the planar and non-planar sectors. We demonstrate the great efficiency of graph-theoretical tools in the systematic study of the possible permutation symmetric integrands. We formulate a general ansatz for the correlation function as a linear combination of all relevant graph topologies, with arbitrary coefficients. Powerful restrictions on the coefficients come from the analysis of the logarithmic divergences of the correlation function in two singular regimes: Euclidean short-distance and Minkowski light-cone limits. We demonstrate that the planar integrand is completely fixed by the procedure up to six loops and probably beyond. In the non-planar sector, we show the absence of non-planar corrections at three loops and we reduce the freedom at four loops to just four constants. Finally, the correlation function/amplitude duality allows us to show the complete agreement of our results with the four-particle planar amplitude in N = 4 SYM.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0521ed3c08cbda7975e9d36373ba5fd031549d01

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. J. Penedones
2. V. Gonçalves
3. M. Costa
4. Shota Komatsu
5. M. Hippel
6. L. Dixon
7. T. Fleury
8. Eric Perlmutter

In Nuclear and High Energy Physics

1. V. Gonçalves
2. M. Costa
3. J. Penedones
4. M. Hippel
5. David Simmons-Duffin
6. C. Sleight
7. L. Dixon
8. Eric Perlmutter

Citations in the corpus

• The full four-loop cusp anomalous dimension in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{do (2019, unknown): “L Q 5≤i≤4+L x 2 1ix 2 2ix 3ix 2 4i Q 5≤i<j≤4+L x 2 ij P(L)(x 1,...,x 4+L). (2.20) 5The additional factor of (−4)L in the denominator comes from the different definition of the integration measure in [49]. – 9 – Here P(L) are homogeneous polynomials in x2 ij of degree (L − 1)(L + 4)/2 whose explicit”
• Bootstrapping an NMHV amplitude through three loops (2014, background): “J H E P 1 0 ( 2 0 1 4 ) 0 6 5 produce the integrand at very high loop order [21–23], but the evaluation of the loop integrals can be quite challenging, in part due to severe infrared divergences.”
• Hexagonalization of correlation functions (2016, methodology): “It would be even nicer if we can use integrability for computing/predicting integrals at four loops and beyond [33] which have never been evaluated.”
• Conformal Regge theory (2012, methodology): “In particular, it would be interesting to study the Regge limit of the four-point function〈 Tr(XZ)(x1) Tr ( XZ ) (x2) Tr ( Y Z ) (x3) Tr ( Y Z ) (x4) 〉 , (114) where X, Y and Z are complex scalar fields of SYM.”