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AZURITE: An algebraic geometry based package for finding bases of loop integrals
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Swiss Fed Inst Technol, Wolfang Pauli Str 27, CH-8093 Zurich, Switzerland..
Univ Southampton, Sch Phys & Astron, Southampton SO17 1BJ, Hants, England.;Swiss Fed Inst Technol, Wolfang Pauli Str 27, CH-8093 Zurich, Switzerland..
Swiss Fed Inst Technol, Wolfang Pauli Str 27, CH-8093 Zurich, Switzerland..
2017 (English)In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 221, p. 203-215Article in journal (Refereed) Published
Abstract [en]

For any given Feynman graph, the set of integrals with all possible powers of the propagators spans a vector space of finite dimension. We introduce the package AZURITE (A ZURich-bred method for finding master InTEgrals), which efficiently finds a basis of this vector space. It constructs the needed integration by-parts (IBP) identities on a set of generalized-unitarity cuts. It is based on syzygy computations and analyses of the symmetries of the involved Feynman diagrams and is powered by the computer algebra systems SINGULAR and MATHEMATICA. It can moreover analytically calculate the part of the IBP identities that is supported on the cuts. In some cases, the basis obtained by AZURITE may be slightly overcomplete.

Program summary

Program Title: AZURITE

Licensing provisions: GNU General Public License (GPL)

Programming language: Wolfram MATHEMATICA version 10.0 or higher

Supplementary material: A manual in the form of a MATHEMATICA notebook

Nature of problem: Determination of a basis of the space of loop integrals spanned by a given Feynman diagram and all of its subdiagrams

Solution method: MATHEMATICA implementation.

Place, publisher, year, edition, pages
2017. Vol. 221, p. 203-215
Keywords [en]
Feynman diagrams, Computational algebraic geometry, Integration-by-parts identities
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:uu:diva-340677DOI: 10.1016/j.cpc.2017.08.013ISI: 000413376800015OAI: oai:DiVA.org:uu-340677DiVA, id: diva2:1180185
Funder
EU, FP7, Seventh Framework Programme, 627521Knut and Alice Wallenberg Foundation, 2015-0083Available from: 2018-02-05 Created: 2018-02-05 Last updated: 2023-05-29Bibliographically approved
In thesis
1. Topics in perturbation theory: From IBP identities to integrands
Open this publication in new window or tab >>Topics in perturbation theory: From IBP identities to integrands
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we present different topics in perturbation theory. We start by introducing the method of integration by parts identities, which reduces a generic Feynman integral to a linear combination of a finite basis of master integrals. In our analysis we make use of the Baikov representation as this form gives a nice framework for generating efficiently the identities needed to reduce integrals. In the second part of the thesis we briefly explain recent developments in the integration of Feynman integrals and present a method to bootstrap the value of p-integrals using constraints from certain limits of conformal integrals. We introduce also another method to obtain p-integrals at l-loops by cutting vacuum diagrams at l+1-loops. In the last part of the thesis we present recent developments in N=4 SYM to compute structure constants. We use perturbation theory to obtain new results that can be tested against this new conjecture. Moreover we use integrability based methods to constrain correlation function of protected operators.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. p. 64
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1805
Keywords
Perturbation theory, Feynman Integrals, Integrable field theories, Correlation functions.
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:uu:diva-381810 (URN)978-91-513-0648-3 (ISBN)
Public defence
2019-06-07, Room Å4001, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2019-05-17 Created: 2019-04-15 Last updated: 2023-05-29

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