Massive Conformal Symmetry and Integrability for Feynman Integrals

Loebbert, Florian; Miczajka, Julian; Müller, Dennis; Münkler, Hagen

doi:10.1103/physrevlett.125.091602

Cited by 37 publications

(95 citation statements)

References 23 publications

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“…In section 3 we contrast the symmetries of scattering amplitudes and Feynman integrals arising in both theories. For option II we illustrate that there is a one-to-one correspondence 1 between off-shell amplitudes and those massive Feynman integrals that were found to feature a massive Yangian [43]. Due to the close similarity to the massless bi-scalar fishnet theory, we thus refer to the theory obtained via scenario II as the massive fishnet (MF) theory.…”

Section: Jhep12(2020)197mentioning

confidence: 96%

“…As opposed to z a andz a , in the latter case the real parameters m a on their own take the role of physical masses. It would be desirable to identify a fishnet-like theory with the latter propagator structure, since massive Feynman diagrams with such difference-mass propagators were recently found to be subject to a Yangian symmetry [43]. This motivates to search for an alternative massive extension of the fishnet theory.…”

Section: Jhep12(2020)197mentioning

confidence: 99%

“…As discussed in more detail in the subsequent section 3, off-shell amplitudes in this theory are in one-to-one correspondence with massive fishnet Feynman integrals that have been found to be Yangian-invariant, cf. [43]. This motivates to refer to the resulting theory as JHEP12(2020)197…”

Section: Double-scaling Limit Of Coulomb-branch N = 4 Sym Theorymentioning

confidence: 99%

“…Recently, however, it was discovered that integrability also features in the building blocks of massive quantum field theories, i.e. on the very right of a potential massive version of the sequence (1.1) [43]. Large families of ubiquitous massive Feynman integrals were found to be invariant under the generators of an extended Yangian.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper we seek the interpretation of the massive Yangian symmetry of Feynman integrals found in [43] as the integrability of a massive quantum field theory. Our guideline is the relation of massless integrability in N = 4 SYM theory and Feynman integrals via the fishnet theory.…”

Section: Introductionmentioning

confidence: 99%

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Massive fishnets

Loebbert

Miczajka

2020

J. High Energ. Phys.

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Recently, infinite families of massive Feynman integrals were found to feature an unexpected Yangian symmetry. In the massless case, similar integrability properties are understood via the interpretation of individual Feynman integrals as correlators in the massless fishnet theory introduced by Gürdoğan and Kazakov. Here we seek for an analogous interpretation of the integrability of massive Feynman integrals. We contrast two approaches to define simple massive quantum field theories in four dimensions. First, we discuss spontaneous symmetry breaking in the massless bi-scalar fishnet theory. We then propose an alternative route to a massive fishnet theory by taking a double-scaling limit of $$ \mathcal{N} $$ N = 4 SYM theory on the Coulomb branch. Both approaches lead to a massive extension of the massless fishnet theory, differing in how masses enter into the propagators. In the latter theory, planar off-shell amplitudes are in one-to-one correspondence with precisely those massive Feynman integrals that were shown to be invariant under the Yangian. This suggests a re-investigation of Coulomb branch $$ \mathcal{N} $$ N = 4 SYM theory with regard to integrability. Finally, we demonstrate that in the case of spontaneous symmetry breaking, the original conformal symmetry leads to soft theorems for scattering amplitudes in the broken phase.

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Section: Jhep12(2020)197mentioning

confidence: 96%

Section: Jhep12(2020)197mentioning

confidence: 99%

Section: Double-scaling Limit Of Coulomb-branch N = 4 Sym Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Massive fishnets

Loebbert

Miczajka

2020

J. High Energ. Phys.

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Hypergeometric Functions and Feynman Diagrams

Kalmykov

Kniehl

Moch

et al. 2021

Texts &Amp; Monographs in Symbolic Computation

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Amplitudes in fishnet theories in diverse dimensions and box ladder diagrams

Bork

Iakhibbaev

Muzhichkov

et al. 2021

J. High Energ. Phys.

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We investigate properties of four-point colour ordered scattering amplitudes in D = 6 fishnet CFT. We show that these amplitudes are related via a very simple relation to their D = 4 counterparts previously considered in the literature. Exploiting this relation, we obtain a closed expression for these amplitudes and investigate its behaviour at weak and strong coupling. As a by product of this investigation, we also obtain a generating function for on-shell D = 6 Box ladder diagrams with l rungs.

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Massive Conformal Symmetry and Integrability for Feynman Integrals

Cited by 37 publications

References 23 publications

Massive fishnets

Massive fishnets

Hypergeometric Functions and Feynman Diagrams

Amplitudes in fishnet theories in diverse dimensions and box ladder diagrams

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