Yangian Bootstrap for Conformal Feynman Integrals

Loebbert, Florian; Müller, Dennis; Münkler, Hagen

doi:10.1103/PhysRevD.101.066006

Yangian Bootstrap for Conformal Feynman Integrals

Florian Loebbert
(
- Humboldt U., Berlin
)
,
Dennis Müller
(
- Bohr Inst.
)
,
Hagen Münkler
(
- Zurich, ETH
)

Dec 11, 2019

22 pages

Published in:

Phys.Rev.D 101 (2020) 6, 066006

Published: Mar 11, 2020

e-Print:

1912.05561 [hep-th]

DOI:

10.1103/PhysRevD.101.066006

Report number:

HU-EP-19/39

View in:

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Abstract: (APS)

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 four dimensions. 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.

Note:

20 pages, v2: minor improvements

String theory, quantum gravity, gauge/gravity duality
loop integral: 4
invariance: Yangian
symmetry: Yangian
symmetry: conformal
Feynman graph
bootstrap
integrability
propagator

References(42)

Figures(18)

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