[{"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Communications in Mathematical Physics","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"oa_version":"Published Version","month":"01","file":[{"success":1,"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"9081","checksum":"6f451f9c2b74bedbc30cf884a3e02670","file_size":790526,"date_created":"2021-02-03T15:00:30Z","file_name":"2021_CommMathPhys_Runkel.pdf","content_type":"application/pdf","date_updated":"2021-02-03T15:00:30Z"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2021-01-01T00:00:00Z","publication_identifier":{"issn":["00103616"],"eissn":["14320916"]},"oa":1,"quality_controlled":"1","page":"83–117","file_date_updated":"2021-02-03T15:00:30Z","publisher":"Springer Nature","article_type":"original","scopus_import":"1","_id":"8816","issue":"1","author":[{"full_name":"Runkel, Ingo","first_name":"Ingo","last_name":"Runkel"},{"last_name":"Szegedy","first_name":"Lorant","full_name":"Szegedy, Lorant","orcid":"0000-0003-2834-5054","id":"7943226E-220E-11EA-94C7-D59F3DDC885E"}],"department":[{"_id":"MiLe"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2020-11-29T23:01:17Z","publication_status":"published","intvolume":"       381","title":"Area-dependent quantum field theory","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).","volume":381,"ddc":["510"],"citation":{"mla":"Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” <i>Communications in Mathematical Physics</i>, vol. 381, no. 1, Springer Nature, 2021, pp. 83–117, doi:<a href=\"https://doi.org/10.1007/s00220-020-03902-1\">10.1007/s00220-020-03902-1</a>.","short":"I. Runkel, L. Szegedy, Communications in Mathematical Physics 381 (2021) 83–117.","ista":"Runkel I, Szegedy L. 2021. Area-dependent quantum field theory. Communications in Mathematical Physics. 381(1), 83–117.","ama":"Runkel I, Szegedy L. Area-dependent quantum field theory. <i>Communications in Mathematical Physics</i>. 2021;381(1):83–117. doi:<a href=\"https://doi.org/10.1007/s00220-020-03902-1\">10.1007/s00220-020-03902-1</a>","apa":"Runkel, I., &#38; Szegedy, L. (2021). Area-dependent quantum field theory. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-020-03902-1\">https://doi.org/10.1007/s00220-020-03902-1</a>","ieee":"I. Runkel and L. Szegedy, “Area-dependent quantum field theory,” <i>Communications in Mathematical Physics</i>, vol. 381, no. 1. Springer Nature, pp. 83–117, 2021.","chicago":"Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-020-03902-1\">https://doi.org/10.1007/s00220-020-03902-1</a>."},"year":"2021","date_updated":"2023-08-04T11:13:35Z","external_id":{"isi":["000591139000001"]},"isi":1,"day":"01","doi":"10.1007/s00220-020-03902-1","abstract":[{"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.","lang":"eng"}]},{"language":[{"iso":"eng"}],"month":"09","oa_version":"Preprint","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"publication":"Communications in Mathematical Physics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1711.04285"}],"oa":1,"publication_identifier":{"eissn":["14320916"],"issn":["00103616"]},"date_published":"2020-09-01T00:00:00Z","type":"journal_article","article_type":"original","publisher":"Springer Nature","page":"1649-1675","quality_controlled":"1","ec_funded":1,"title":"Sandpile solitons via smoothing of superharmonic functions","intvolume":"       378","publication_status":"published","date_created":"2020-08-30T22:01:13Z","department":[{"_id":"TaHa"}],"article_processing_charge":"No","author":[{"full_name":"Kalinin, Nikita","first_name":"Nikita","last_name":"Kalinin"},{"id":"35084A62-F248-11E8-B48F-1D18A9856A87","full_name":"Shkolnikov, Mikhail","orcid":"0000-0002-4310-178X","last_name":"Shkolnikov","first_name":"Mikhail"}],"issue":"9","_id":"8325","scopus_import":"1","volume":378,"acknowledgement":"We thank Andrea Sportiello for sharing his insights on perturbative regimes of the Abelian sandpile model which was the starting point of our work. We also thank Grigory Mikhalkin, who encouraged us to approach this problem. We thank an anonymous referee. Also we thank Misha Khristoforov and Sergey Lanzat who participated on the initial state of this project, when we had nothing except the computer simulation and pictures. We thank Mikhail Raskin for providing us the code on Golly for faster simulations. Ilia Zharkov, Ilia Itenberg, Kristin Shaw, Max Karev, Lionel Levine, Ernesto Lupercio, Pavol Ševera, Yulieth Prieto, Michael Polyak, Danila Cherkashin asked us a lot of questions and listened to us; not all of their questions found answers here, but we are going to treat them in subsequent papers.","abstract":[{"text":"Let 𝐹:ℤ2→ℤ be the pointwise minimum of several linear functions. The theory of smoothing allows us to prove that under certain conditions there exists the pointwise minimal function among all integer-valued superharmonic functions coinciding with F “at infinity”. We develop such a theory to prove existence of so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo, G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the phenomena of the identity in the sandpile group for planar domains where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we apply the wave operator (that is why we call them solitons), and can interact, forming triads and nodes. ","lang":"eng"}],"doi":"10.1007/s00220-020-03828-8","arxiv":1,"day":"01","isi":1,"external_id":{"arxiv":["1711.04285"],"isi":["000560620600001"]},"date_updated":"2023-08-22T09:00:03Z","citation":{"ista":"Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. 378(9), 1649–1675.","short":"N. Kalinin, M. Shkolnikov, Communications in Mathematical Physics 378 (2020) 1649–1675.","mla":"Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 9, Springer Nature, 2020, pp. 1649–75, doi:<a href=\"https://doi.org/10.1007/s00220-020-03828-8\">10.1007/s00220-020-03828-8</a>.","chicago":"Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-020-03828-8\">https://doi.org/10.1007/s00220-020-03828-8</a>.","ieee":"N. Kalinin and M. Shkolnikov, “Sandpile solitons via smoothing of superharmonic functions,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 9. Springer Nature, pp. 1649–1675, 2020.","apa":"Kalinin, N., &#38; Shkolnikov, M. (2020). Sandpile solitons via smoothing of superharmonic functions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-020-03828-8\">https://doi.org/10.1007/s00220-020-03828-8</a>","ama":"Kalinin N, Shkolnikov M. Sandpile solitons via smoothing of superharmonic functions. <i>Communications in Mathematical Physics</i>. 2020;378(9):1649-1675. doi:<a href=\"https://doi.org/10.1007/s00220-020-03828-8\">10.1007/s00220-020-03828-8</a>"},"year":"2020"}]