Yangian symmetry for bi-scalar loop amplitudes

Chicherin, Dmitry; Казаков, Владимир; Loebbert, Florian; Müller, Dennis; Zhong, De-liang

doi:10.1007/jhep05(2018)003

Cited by 65 publications

(148 citation statements)

References 82 publications

(151 reference statements)

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“…Facing these problems, theorists are challenged to identify new methods to evaluate these integrals and to unveil their deeper mathematical structure. Recently a new infinite dimensional Yangian symmetry was identified for a large class of so-called fishnet Feynman graphs [1,2]. In the present paper we explore this connection between Feynman integrals and the theory of integrable models, which play a crucial role for developing analytical methods in all areas of physics.…”

Section: Introductionmentioning

confidence: 93%

“…Being a member of the class of fishnet Feynman graphs discussed in [1,2], also the double box integral is invariant under the conformal Yangian algebra: (75) In this case conformal symmetry dictates that I 3,3 is of the formÎ…”

Section: Six-point Double Boxmentioning

confidence: 99%

“…Integrability is very constraining and if properly understood one can expect that it completely fixes physical observables through the underlying symmetry constraints. In [1,2] it was shown that certain Feynman graphs provide a means to obtain an infinite class of Yangian invariants. In the previous section we have shown that these Yangian invariants have a fine structure, i.e.…”

Section: Yangian Invariants and Mellin-barnes Integralsmentioning

confidence: 99%

“…The double box PDEs given in (78) are obtained by using the evaluation parameters (cf. [1]) s j = − 0, 1, 2, 2, 3, 4 j .…”

Section: Appendix E: Hexagon Pdesmentioning

confidence: 99%

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Yangian bootstrap for conformal Feynman integrals

Müller²,

2020

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We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the D-dimensional box integral with generic propagator powers is completely fixed by its symmetries to be a particular linear combination of Appell hypergeometric functions. In this context the Bloch-Wigner function arises as a special Yangian invariant in 4D. The bootstrap procedure for the box integral is naturally structured in algorithmic form. We then discuss the Yangian constraints for the six-point double box integral as well as for the related hexagon. For the latter we argue that the constraints are solved by a set of generalized Lauricella functions and we comment on complications in identifying the integral as a certain linear combination of these. Finally, we elaborate on the close relation to the Mellin-Barnes technique and argue that it generates Yangian invariants as sums of residues. *

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Section: Introductionmentioning

confidence: 93%

Section: Six-point Double Boxmentioning

confidence: 99%

Section: Yangian Invariants and Mellin-barnes Integralsmentioning

confidence: 99%

“…The double box PDEs given in (78) are obtained by using the evaluation parameters (cf. [1]) s j = − 0, 1, 2, 2, 3, 4 j .…”

Section: Appendix E: Hexagon Pdesmentioning

confidence: 99%

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Yangian bootstrap for conformal Feynman integrals

Müller²,

2020

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“…We would like to emphasize here that given (6.32), (6.36) is in fact exact coupling. We can further this argument by expanding around ν = 0 (assuming that the ν−integral is peaked around the origin 15 and neglecting the effect of the poles) 16 ,…”

Section: Further Ementioning

confidence: 99%

On the Regge limit of Fishnet correlators

Chowdhury

Haldar

Sen

2019

J. High Energ. Phys.

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We study the Regge trajectories of the Mellin amplitudes of the 0−, 1− and 2− magnon correlators of the Fishnet theory. Since fishnet theory is both integrable and conformal, the correlation functions are known exactly. We find that while for 0 and 1 magnon correlators, the Regge poles can be exactly determined as a function of coupling, 2-magnon correlators can only be dealt with perturbatively. We evaluate the resulting Mellin amplitudes at weak coupling, while for strong coupling we do an order of magnitude calculation. II Superstring theory [5], the Regge limit of the scattering amplitude scales as s 2+ α t 2 which denotes graviton dominance in the high energy limit (t is negative). Similarly for QCD, one can see from [6] that the LLA (leading log approximation) contribution to the Regge limit comes from,(1.5)The same can be shown in a perturbative manner for the N = 4 SYM [7] for which in weak coupling,In contrast, for the fishnet theories under consideration, we find that for the 0, 1, 2−magnon cases, in the weak coupling, the leading Regge theory is dominated by,respectively. This is expected to be connected with the inherent non-unitarity of the theory so that the effective exchanges in the Regge limit has negative spins. In this case, the LLA contribution is expected 1 Unlike other theories, where the Regge trajectories are only known in certain limits (say the weak coupling limit), here the trajectories are exact functions of the coupling ξ.

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Symmetries of Maldacena-Wilson Loops from Integrable String Theory

Münkler

2018

Springer Theses

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This thesis discusses hidden symmetries within N " 4 supersymmetric Yang-Mills theory or its AdS/CFT dual, string theory in AdS 5ˆS 5 . Here, we focus on the Maldacena-Wilson loop, which is a suitable object for this study since its vacuum expectation value is finite for smooth contours and the conjectured duality to scattering amplitudes provides a conceptual path to transfer its symmetries to other observables. Its strong-coupling description via minimal surfaces in AdS 5 allows to construct the symmetries from the integrability of the underlying classical string theory. This approach has been utilized before to derive a strong-coupling Yangian symmetry of the Maldacena-Wilson loop and describe equiareal deformations of minimal surfaces in AdS 3 . These two findings are connected and extended in the present thesis.In order to discuss the symmetries systematically, we first discuss the symmetry structure of the underlying string model. The discussion can be generalized to the discussion of generic symmetric space models. For these, we find that the symmetry which generates the equiareal deformations of minimal surfaces in AdS 3 has a central role in the symmetry structure of the model: It acts as a raising operator on the infinite tower of conserved charges, thus generating the spectral parameter, and can be employed to construct all symmetry variations from the global symmetry of the model. It is thus referred to as the master symmetry of symmetric space models. Additionally, the algebra of the symmetry variations and the conserved charges is worked out.For the concrete case of minimal surfaces in AdS 5 , we discuss the deformation of the four-cusp solution, which provides the dual description of the four-gluon scattering amplitude. This marks the first step toward transferring the master symmetry to scattering amplitudes. Moreover, we compute the master and Yangian symmetry variations of generic, smooth boundary curves. The results leads to a couplingdependent generalization of the master symmetry, which constitutes a symmetry of the Maldacena-Wilson loop at any value of the coupling constant. Our discussion clarifies why previous attempts to transfer the deformations of minimal surfaces in AdS 3 to weak coupling were unsuccessful. We discuss several attempts to transfer the Yangian symmetry to weak or arbitrary coupling, but ultimately conclude that a Yangian symmetry of the Maldacena-Wilson loop seems not to be present.The situation changes when we consider Wilson loops in superspace, which are the natural supersymmetric generalizations of the Maldacena-Wilson loop. Substantial evidence for the Yangian invariance of their vacuum expectation value has been provided at weak coupling and the description of the operator as well as its weak-coupling Yangian invariance were subsequently established in parallel to the work on this thesis. We discuss the strong-coupling counterpart of this finding, where the Wilson loop in superspace is described by minimal surfaces in the superspace of type IIB superstring theory i...

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Yangian symmetry for bi-scalar loop amplitudes

Cited by 65 publications

References 82 publications

Yangian bootstrap for conformal Feynman integrals

Yangian bootstrap for conformal Feynman integrals

On the Regge limit of Fishnet correlators

Symmetries of Maldacena-Wilson Loops from Integrable String Theory

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