Categorification of algebraic quantum field theories

Marco Benini; Marco Perin; Alexander Schenkel; Lukas Woike

doi:10.1007/s11005-021-01371-8

Categorification of algebraic quantum field theories

Marco Benini, Marco Perin, Alexander Schenkel^*, Lukas Woike

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

11 Citationer (Scopus)

Abstract

This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

Originalsprog	Engelsk
Artikelnummer	35
Tidsskrift	Letters in Mathematical Physics
Vol/bind	111
Udgave nummer	2
ISSN	0377-9017
DOI	https://doi.org/10.1007/s11005-021-01371-8
Status	Udgivet - 2021
Udgivet eksternt	Ja

Bibliografisk note

Funding Information:
We would like to thank Simen Bruinsma, Chris Fewster, Ignacio Lopez Franco, Klaus Fredenhagen, Owen Gwilliam, Theo Johnson-Freyd and Robert Laugwitz for useful discussions about this work. We also would like to thank the referees for their detailed comments and suggestions that helped us to improve this manuscript. M.B. gratefully acknowledges the financial support of the National Group of Mathematical Physics GNFM-INdAM (Italy). M.P. is supported by a PhD scholarship (RGFEA180270) of the Royal Society (UK). A.S. gratefully acknowledges the financial support of the Royal Society (UK) through a Royal Society University Research Fellowship (UF150099), a Research Grant (RG160517) and two Enhancement Awards (RGFEA180270 and RGFEA201051). L.W. is supported by the RTG 1670 “Mathematics inspired by String Theory and Quantum Field Theory.”

Funding Information:
We would like to thank Simen Bruinsma, Chris Fewster, Ignacio Lopez Franco, Klaus Fredenhagen, Owen Gwilliam, Theo Johnson-Freyd and Robert Laugwitz for useful discussions about this work. We also would like to thank the referees for their detailed comments and suggestions that helped us to improve this manuscript. M.B. gratefully acknowledges the financial support of the National Group of Mathematical Physics GNFM-INdAM (Italy). M.P. is supported by a PhD scholarship (RGF\ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\backslash $$\end{document} EA\ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\backslash $$\end{document} 180270) of the Royal Society (UK). A.S. gratefully acknowledges the financial support of the Royal Society (UK) through a Royal Society University Research Fellowship (UF150099), a Research Grant (RG160517) and two Enhancement Awards (RGF\ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\backslash $$\end{document} EA\ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\backslash $$\end{document} 180270 and RGF\ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\backslash $$\end{document} EA\ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\backslash $$\end{document} 201051). L.W. is supported by the RTG 1670 ?Mathematics inspired by String Theory and Quantum Field Theory.?

Publisher Copyright:
© 2021, The Author(s).

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Citationsformater

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title = "Categorification of algebraic quantum field theories",

abstract = "This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen{\textquoteright}s universal algebra is developed and also computed for simple examples of 2AQFTs.",

keywords = "2-Categories, 2-Operads, Algebraic quantum field theory, Categorified orbifold theories, Local-to-global extensions, Locally presentable linear categories, Quasi-coherent sheaves",

author = "Marco Benini and Marco Perin and Alexander Schenkel and Lukas Woike",

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AU - Perin, Marco

AU - Schenkel, Alexander

AU - Woike, Lukas

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KW - 2-Categories

KW - 2-Operads

KW - Algebraic quantum field theory

KW - Categorified orbifold theories

KW - Local-to-global extensions

KW - Locally presentable linear categories

KW - Quasi-coherent sheaves

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DO - 10.1007/s11005-021-01371-8

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