Single-valued integration and double copy
| Autor: | Francis Brown, Clément Dupont |
|---|---|
| Přispěvatelé: | Mathematical Institute [Oxford] (MI), University of Oxford [Oxford], Institut des Hautes Etudes Scientifiques (IHES), IHES, Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics Differential form General Mathematics Modular form FOS: Physical sciences 01 natural sciences Volume integral Mathematics - Algebraic Geometry 0103 physical sciences FOS: Mathematics De Rham cohomology Number Theory (math.NT) 0101 mathematics Algebraic Geometry (math.AG) Projective variety Mathematics Conjecture Mathematics - Number Theory 010308 nuclear & particles physics [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Applied Mathematics 010102 general mathematics [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] Moduli space High Energy Physics - Theory (hep-th) Pairing [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] |
| Zdroj: | Journal für die reine und angewandte Mathematik Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2021, pp.145-196 Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2021, 775, pp.145-196. ⟨10.1515/crelle-2020-0042⟩ |
| ISSN: | 0075-4102 1435-5345 |
| Popis: | We study a single-valued integration pairing between differential forms and dual differential forms which subsumes some classical constructions in mathematics and physics. It can be interpreted as a $p$-adic period pairing at the infinite prime. The single-valued integration pairing is defined by transporting the action of complex conjugation from singular to de Rham cohomology via the comparison isomorphism. We show how quite general families of period integrals admit canonical single-valued versions and prove some general formulas for them. This implies an elementary 'double copy' formula expressing certain singular volume integrals over the complex points of a smooth projective variety as a quadratic expression in ordinary period integrals of half the dimension. We provide several examples, including non-holomorphic modular forms, archimedean N\'{e}ron-Tate heights on curves, single-valued multiple zeta values and polylogarithms. In a sequel to this paper we apply this formalism to the moduli space of curves of genus zero with marked points, to deduce a recent conjecture due to Stieberger in string perturbation theory, which states that closed string amplitudes are the single-valued projections of open string amplitudes. Comment: The results are unchanged. We made some minor corrections and added several remarks and clarifications |
| Databáze: | OpenAIRE |
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