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Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
TU Kaiserslautern, Dept Math, D-67663 Kaiserslautern, Germany.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
Univ Southampton, Sch Phys & Astron, Southampton SO17 1BJ, Hants, England.
TU Kaiserslautern, Dept Math, D-67663 Kaiserslautern, Germany.
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2018 (English)In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 98, no 2, article id 025023Article in journal (Refereed) Published
Abstract [en]

Integration-by-parts identities between loop integrals arise from the vanishing integration of total derivatives in dimensional regularization. Generic choices of total derivatives in the Baikov or parametric representations lead to identities which involve dimension shifts. These dimension shifts can be avoided by imposing a certain constraint on the total derivatives. The solutions of this constraint turn out to be a specific type of syzygies which correspond to logarithmic vector fields along the Gram determinant formed of the independent external and loop momenta. We present an explicit generating set of solutions in Baikov representation, valid for any number of loops and external momenta, obtained from the Laplace expansion of the Gram determinant. We provide a rigorous mathematical proof that this set of solutions is complete. This proof relates the logarithmic vector fields in question to ideals of submaximal minors of the Gram matrix and makes use of classical resolutions of such ideals.

Place, publisher, year, edition, pages
2018. Vol. 98, no 2, article id 025023
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
URN: urn:nbn:se:uu:diva-361998DOI: 10.1103/PhysRevD.98.025023ISI: 000439976300007OAI: oai:DiVA.org:uu-361998DiVA, id: diva2:1253658
Funder
EU, Horizon 2020, 725110Knut and Alice Wallenberg Foundation, 2015-0083EU, European Research Council, 648630 IQFTAvailable from: 2018-10-05 Created: 2018-10-05 Last updated: 2019-04-15Bibliographically 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: 2019-06-17

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Georgoudis, Alessandro

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