TY  - JOUR
AU  - Pögel, Sebastian
AU  - Wang, Xing
AU  - Weinzierl, Stefan
AU  - Wu, Konglong
AU  - Xu, Xiaofeng
TI  - Self-dualities and Galois symmetries in Feynman integrals
JO  - Journal of high energy physics
VL  - 2024
IS  - 9
SN  - 1029-8479
CY  - Heidelberg
PB  - Springer
M1  - PUBDB-2025-00326
M1  - arXiv:2407.08799
SP  - 84
PY  - 2024
N1  - 41 pages, v2: version to be published
AB  - It is well-known that all Feynman integrals within a given family can be expressed as a finite linear combination of master integrals. The master integrals naturally group into sectors. Starting from two loops, there can exist sectors made up of more than one master integral. In this paper we show that such sectors may have additional symmetries. First of all, self-duality, which was first observed in Feynman integrals related to Calabi-Yau geometries, often carries over to non-Calabi-Yau Feynman integrals. Secondly, we show that in addition there can exist Galois symmetries relating integrals. In the simplest case of two master integrals within a sector, whose definition involves a square root r, we may choose a basis (I<sub>1</sub>, I<sub>2</sub>) such that I<sub>2</sub> is obtained from I<sub>1</sub> by the substitution r → −r. This pattern also persists in sectors, which a priori are not related to any square root with dependence on the kinematic variables. We show in several examples that in such cases a suitable redefinition of the integrals introduces constant square roots like  √3 . The new master integrals are then again related by a Galois symmetry, for example the substitution  √3  →  −√3 . To handle the case where the argument of a square root would be a perfect square we introduce a limit Galois symmetry. Both self-duality and Galois symmetries constrain the differential equation.
KW  - Differential and Algebraic Geometry (autogen)
KW  - Higher Order Electroweak Calculations (autogen)
KW  - Higher-Order Perturbative Calculations (autogen)
KW  - Scattering Amplitudes (autogen)
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001352030300002
DO  - DOI:10.1007/JHEP09(2024)084
UR  - https://bib-pubdb1.desy.de/record/622463
ER  -