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Izvestiya: Mathematics, 2016, Volume 80, Issue 5, Pages 813–848
DOI: https://doi.org/10.1070/IM8492 (Mi im8492) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Feynman amplitudes and limits of heights

O. Aminia, S. J. Bloch, J. I. Burgos Gilb, J. Fresánc

a CNRS--DMA, École Normale Supérieure, Paris, France
b Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, Madrid, Spain
c Eidgenössische Technische Hochschule Zürich, Zürich, Switzerland
English version PDF (498 kB) Citations (9)
References:
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DOI: https://doi.org/10.1070/IM8492
Abstract: We investigate from a mathematical perspective how Feynman amplitudes appear in the low-energy limit of string amplitudes. In this paper, we prove the convergence of the integrands. We derive this from results describing the asymptotic behaviour of the height pairing between degree-zero divisors, as a family of curves degenerates. These are obtained by means of the nilpotent orbit theorem in Hodge theory.
Keywords: Feynman amplitudes, low-energy limit, asymptotics of the archimedean height pairing, Symanzik polynomials, nilpotent orbit theorem, biextension mixed Hodge structures, regularized Green functions.
Funding agency Grant number
Ministerio de Economía y Competitividad de España MTM2013--42135--P
SEV--2015--0554
Deutsche Forschungsgemeinschaft SFB 1085
Swiss National Science Foundation 200021--150099
200020--162928
J. I. Burgos Gil was partially supported by the MINECO research projects MTM2013–42135–P and ICMAT Severo Ochoa project SEV–2015–0554, and the DFG project SFB 1085 “Higher Invariants”. J. Fresán acknowledges support from the SNFS grants 200021–150099 and 200020–162928.
Received: 15.12.2015
Revised: 18.04.2016
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2016, Volume 80, Issue 5, Pages 5–40
DOI: https://doi.org/10.4213/im8492
Bibliographic databases:
Document Type: Article
UDC: 512.73, 512.72, 512.721, 512.75
MSC: 32G20, 14D05, 37P30, 81Q30, 81T30
Language: English
Original paper language: Russian
Citation: O. Amini, S. J. Bloch, J. I. Burgos Gil, J. Fresán, “Feynman amplitudes and limits of heights”, Izv. RAN. Ser. Mat., 80:5 (2016), 5–40; Izv. Math., 80:5 (2016), 813–848
Citation in format AMSBIB
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\paper Feynman amplitudes and limits of heights
\jour Izv. RAN. Ser. Mat.
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:66
    First page:30
     
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