Gluing Ladder Feynman Diagrams into Fishnets

Basso, Benjamin; Dixon, Lance J.

doi:10.1103/physrevlett.119.071601

Cited by 96 publications

(154 citation statements)

References 74 publications

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“…The form (1.2) of the perturbative octagon carries some resemblance to the result of Basso and Dixon [19] obtained for the fishnet limit of the N = 4 SYM [20] 2 . The analytic expression obtained in [19] for the fishnet has the form of a single determinant of ladders, while bootstraping the Ansatz (1.2) one obtains [18] a series in the minors of the semi-infinite matrix…”

Section: Introductionsupporting

confidence: 65%

“…(1. 19) as well as factors depending on ξ = − 1 2 log zz and the bridge length . • The symmetric bilocal factorsH ab (u, v) are produced by the diagonal part of the hexagon weights in mirror-mirror kinematics 20) where x = x(u) and y = x(v).…”

Section: The Octagon Form Factormentioning

confidence: 99%

“…In [18], the octagon was expanded in a basis of minors of the matrix (1.4). In particular, the lowest loop order n-particle contribution is proportional to the determinant of the matrix (1.4) restricted to the first n rows and columns, which has been identified in [19] with the Feynman integral for an n × n fishnet,…”

Section: Fishnetsmentioning

confidence: 99%

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The octagon as a determinant

Kostov

Petkova

Serban

2019

J. High Energ. Phys.

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The computation of a certain class of four-point functions of heavily charged BPS operators boils down to the computation of a special form factor -the octagon. In this paper, which is an extended version of the short note [1], we derive a non-perturbative formula for the square of the octagon as the determinant of a semi-infinite skew-symmetric matrix. We show that perturbatively in the weak coupling limit the octagon is given by a determinant constructed from the polylogarithms evaluating ladder Feynman graphs. We also give a simple operator representation of the octagon in terms of a vacuum expectation value of massless free bosons or fermions living in the rapidity plane. arXiv:1905.11467v1 [hep-th] 27 May 20191 The fact that the sum over virtual particles can be written as a Fredholm pfaffian has been noticed before in [14].(1.7) 2 The integrability of the fishnet Feynman graphs has been first established by A. Zamolodchikov [21]. 3 By Zhukovsky plane we mean the rapidity plane with two simple branch points at u = ±2g. A similar operator representation has been proposed in [22] for the three-point function of non-BPS operators.

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Section: Introductionsupporting

confidence: 65%

Section: The Octagon Form Factormentioning

confidence: 99%

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The octagon as a determinant

Kostov

Petkova

Serban

2019

J. High Energ. Phys.

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“…The good agreement found for integral 3.6L4P.b.I is the first numerical confirmation of the analytical expression obtained in ref. [110].…”

Section: Multi-loop Finite Integralsmentioning

confidence: 99%

Numerical Loop-Tree Duality: contour deformation and subtraction

Capatti

Hirschi

Kermanschah

et al. 2020

J. High Energ. Phys.

107

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We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour deformation automatically satisfies all constraints without the need for fine-tuning. We demonstrate that our construction is systematic and efficient by applying it to more than 100 examples of finite scalar integrals featuring up to six loops. We also showcase a first step towards handling non-integrable singularities by applying our work to one-loop infrared divergent scalar integrals and to the one-loop amplitude for the ordered production of two and three photons. This requires the combination of our contour deformation with local counterterms that regulate soft, collinear and ultraviolet divergences. This work is an important step towards computing higher-order corrections to relevant scattering cross-sections in a fully numerical fashion. arXiv:1912.09291v1 [hep-ph] 19 Dec 2019 7 Results 53 7.1 Multi-loop finite integrals 54 7.2 Divergent one-loop four-and five-point scalar integrals 69 7.3 One-loop amplitude for qq → γ 1 γ 2 and qq → γ 1 γ 2 γ 3 69 -i -8 Conclusion 74 9 Acknowledgements 75 A Loop-Tree Duality example at two loops 76 B Expression for the qq → γ 1 γ 2 γ 3 amplitude and its counterterms 79 C Loop-Tree Duality with raised propagators 80 1 As discussed in ref.[83], our final expression in eq. (2.5) is also correct in the case of complex-valued external momenta, due to the fact that the right-most column of the matrix appearing in eq. (2.4) does not include the imaginary part Im[p 0 i ] of the external momenta. We note however, that the correct interpretation of the absence of this term in eq. (2.4) for complex-valued external kinematics is that the energy integrals are no longer performed along the real line but instead along a path including only one out of the two complex energy solutions of each propagator.3)The quantity ∇ k η( k), henceforth denoted as ∇η, is the outward pointing normal vector to the surface η( k) = 0. The contour deformation is defined in the (3n)-dimensional complex space and we parametrise it as k − i κ( k). It must satisfy constraints affecting two of its key characteristics, the direction and magnitude of the vector field κ( k):Direction: The deformation vector κ( k) must induce a sign of the imaginary part of the E-surface equation that matches the sign enforced by the causal prescription whenever k lies on a singular E-surfaces. This imposes conditions on the direction of the vector field κ( k). We derive these conditions by comparing the sign of the LTD prescription

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“…Fishnet CFTs with the hallmarks of integrability also exist in diverse dimensions [27,28] and arise from non-integrable gauge theories [29]. Furthermore, many of the Feynman integrals of FCFT play an important role in other integrable QFTs like N = 4 SYM (cf., [30,31]).…”

Section: Introductionmentioning

confidence: 99%

Twistor fishnets

Adamo

Jaitly

2020

J. Phys. A: Math. Theor.

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Four-dimensional conformal fishnet theory is an integrable scalar theory which arises as a double scaling limit of γ-deformed maximally supersymmetric Yang-Mills. We give a perturbative reformulation of γ-deformed super-Yang-Mills theory in twistor space, and implement the double scaling limit to obtain a twistor description of conformal fishnet theory. The conformal fishnet theory retains an abelian gauge symmetry on twistor space which is absent in space-time, allowing us to obtain cohomological formulae for scattering amplitudes that manifest conformal invariance. We study various classes of scattering amplitudes in twistor space with this formalism.

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Gluing Ladder Feynman Diagrams into Fishnets

Cited by 96 publications

References 74 publications

The octagon as a determinant

The octagon as a determinant

Numerical Loop-Tree Duality: contour deformation and subtraction

Twistor fishnets

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