---
_id: '8816'
abstract:
- lang: eng
text: Area-dependent quantum field theory is a modification of two-dimensional topological
quantum field theory, where one equips each connected component of a bordism with
a positive real number—interpreted as area—which behaves additively under glueing.
As opposed to topological theories, in area-dependent theories the state spaces
can be infinite-dimensional. We introduce the notion of regularised Frobenius
algebras in Hilbert spaces and show that area-dependent theories are in one-to-one
correspondence to commutative regularised Frobenius algebras. We also provide
a state sum construction for area-dependent theories. Our main example is two-dimensional
Yang–Mills theory with compact gauge group, which we treat in detail.
acknowledgement: The authors thank Yuki Arano, Nils Carqueville, Alexei Davydov, Reiner
Lauterbach, Pau Enrique Moliner, Chris Heunen, André Henriques, Ehud Meir, Catherine
Meusburger, Gregor Schaumann, Richard Szabo and Stefan Wagner for helpful discussions
and comments. We also thank the referees for their detailed comments which significantly
improved the exposition of this paper. LS is supported by the DFG Research Training
Group 1670 “Mathematics Inspired by String Theory and Quantum Field Theory”. Open
access funding provided by Institute of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Ingo
full_name: Runkel, Ingo
last_name: Runkel
- first_name: Lorant
full_name: Szegedy, Lorant
id: 7943226E-220E-11EA-94C7-D59F3DDC885E
last_name: Szegedy
orcid: 0000-0003-2834-5054
citation:
ama: Runkel I, Szegedy L. Area-dependent quantum field theory. Communications
in Mathematical Physics. 2021;381(1):83–117. doi:10.1007/s00220-020-03902-1
apa: Runkel, I., & Szegedy, L. (2021). Area-dependent quantum field theory.
Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-020-03902-1
chicago: Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.”
Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-020-03902-1.
ieee: I. Runkel and L. Szegedy, “Area-dependent quantum field theory,” Communications
in Mathematical Physics, vol. 381, no. 1. Springer Nature, pp. 83–117, 2021.
ista: Runkel I, Szegedy L. 2021. Area-dependent quantum field theory. Communications
in Mathematical Physics. 381(1), 83–117.
mla: Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” Communications
in Mathematical Physics, vol. 381, no. 1, Springer Nature, 2021, pp. 83–117,
doi:10.1007/s00220-020-03902-1.
short: I. Runkel, L. Szegedy, Communications in Mathematical Physics 381 (2021)
83–117.
date_created: 2020-11-29T23:01:17Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-04T11:13:35Z
day: '01'
ddc:
- '510'
department:
- _id: MiLe
doi: 10.1007/s00220-020-03902-1
external_id:
isi:
- '000591139000001'
file:
- access_level: open_access
checksum: 6f451f9c2b74bedbc30cf884a3e02670
content_type: application/pdf
creator: dernst
date_created: 2021-02-03T15:00:30Z
date_updated: 2021-02-03T15:00:30Z
file_id: '9081'
file_name: 2021_CommMathPhys_Runkel.pdf
file_size: 790526
relation: main_file
success: 1
file_date_updated: 2021-02-03T15:00:30Z
has_accepted_license: '1'
intvolume: ' 381'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 83–117
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- '14320916'
issn:
- '00103616'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Area-dependent quantum field theory
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 381
year: '2021'
...