Polylogarithms from the Bound State S-matrix

Leeuw, Marius de; Eden, Burkhard; Plat, Dennis le; Meier, Tim

doi:10.1007/978-981-15-7775-8_4

Cited by 3 publications

(7 citation statements)

References 15 publications

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“…Note that the bar over χ means conjugation of all the indices of the fields φ 1 ↔ φ 2 and ψ 1 ↔ ψ 2 . The foremost sum in the expression (2.18) is over the dressings, in other words, the naive basis of the bound states has to be modified by inserting some Z-markers in two different ways denoted plus and minus (the factor of half is because one has to take the average, see [41,42] for a recent discussion about Z-markers). The rule for the plus dressing is the following…”

Section: Two-particle Contributions At Two-loopmentioning

confidence: 99%

“…The only known complet analytically evaluation of a two-particle contribution is the simpler case of the tree-level propagator contribution for fishnet theories appearing in [46]. It should be possible to extend these tecniques to more complicated integrals or greatly simplifies the integrand, we hope to address these questions in the future and some recent progresses in evaluating these integrals analytically can be found in [41,42]. In this work, we only generate power series from integrability and fit the results with a basis of two-loop integrals that we evaluate as described in the appendix B.…”

Section: S J 4 / a E W Y P C 2 < / L A T E X I T > < L A T E X I T S H A 1 _ B A S E 6 4 = " C K 8 P D C + E K Z H 4 N U M S P + Z G 7 R mentioning

confidence: 99%

“…The basis of integrals we have used consists of the ladder the fermionic transformations of the particles involve powers of Z-markers, thus the Z-marker prescription is related somehow to supersymmetry. Notice that they are responsible for removing the square root cuts of all integrability integrands and in this sense the prescription is almost unique [41,42]. From the relation to perturbative calculations it is possible to understand qualitatively the increasing of Rcharge structures of the multi-particle integrability contribution.…”

Section: S J 4 / a E W Y P C 2 < / L A T E X I T > < L A T E X I T S H A 1 _ B A S E 6 4 = " C K 8 P D C + E K Z H 4 N U M S P + Z G 7 R mentioning

confidence: 99%

“…It will be great to develop a deeper understanding of the integrability integrand. An interesting analysis of the one loop integrand has been put forward in [41,42]. The one loop result has been known for a while however the approach taken in that papers might shed some light on the space of functions that the integrand integrates to.…”

Section: Jhep07(2020)030mentioning

confidence: 99%

“…So, in this work, we have computed the integrability contributions for five points and then reduced the result to four by identifying a pair of points. This can be improved by a deeper understanding of the integrability integrand and by performing some analytical integrations, see [41,42] for interesting progress in this direction.…”

Section: Introductionmentioning

confidence: 99%

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Decagon at two loops

Fleury

Gonçalves

2020

J. High Energ. Phys.

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We have computed the simplest five point function in $$ \mathcal{N} $$ N = 4 SYM at two loops using the hexagonalization approach to correlation functions. Along the way we have determined all two-particle mirror contributions at two loops and we have computed all the integrals involved in the final result. As a test of our results we computed a few four-point functions and they agree with the perturbative results computed previously. We have also obtained l loop results for some parts of the two-particle contributions with l arbitrary. We also derive differential equations for a class of integrals that should appear at higher loops in the five point function.

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Section: Two-particle Contributions At Two-loopmentioning

confidence: 99%

Section: S J 4 / a E W Y P C 2 < / L A T E X I T > < L A T E X I T S H A 1 _ B A S E 6 4 = " C K 8 P D C + E K Z H 4 N U M S P + Z G 7 R mentioning

confidence: 99%

Section: S J 4 / a E W Y P C 2 < / L A T E X I T > < L A T E X I T S H A 1 _ B A S E 6 4 = " C K 8 P D C + E K Z H 4 N U M S P + Z G 7 R mentioning

confidence: 99%

Section: Jhep07(2020)030mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Decagon at two loops

Fleury

Gonçalves

2020

J. High Energ. Phys.

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Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution

Bork,

Onishchenko

2019

Preprint

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We present the technique for resummation of flux tube excitations series arising in pentagon operator expansion program for polygonal Wilson loops in N = 4 SYM. Here we restrict ourselves with contributions of one-particle effective states and consider as a particular example NMHV 6 amplitude at one-loop. The presented technique is also applicable at higher loops for one effective particle contributions and has the potential for generalization for contributions with more effective particles.

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Multi-particle finite-volume effects for hexagon tessellations

Leeuw¹,

Eden²,

Plat³

et al. 2019

Preprint

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Correlation functions of gauge-invariant composite operators in N = 4 super Yang-Mills theory can be computed by integrability using triangulations. The elementary tile in this process is the hexagon, which should be glued by appropriately inserting resolutions of the identity involving virtual ("mirror") magnons. We consider this problem for five-point functions of protected operators. At one-loop in the 't Hooft coupling, it is necessary to glue three adjacent tiles which involves two virtual magnons scattering among each other. We show that the result can be simplified by using an adapted mirror rotation and employing appropriate summation techniques. The mirror-particle contributions then yield hyperlogarithms of weight two. Finally, we use these results to investigate braiding prescriptions introduced in earlier work on the problem.

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Polylogarithms from the Bound State S-matrix

Cited by 3 publications

References 15 publications

Decagon at two loops

Decagon at two loops

Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution

Multi-particle finite-volume effects for hexagon tessellations

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