[{"has_accepted_license":"1","oa_version":"Published Version","year":"2021","article_type":"original","publication_identifier":{"issn":["00103616"],"eissn":["14320916"]},"scopus_import":"1","external_id":{"isi":["000591139000001"]},"date_updated":"2023-08-04T11:13:35Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_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."}],"date_published":"2021-01-01T00:00:00Z","file":[{"file_name":"2021_CommMathPhys_Runkel.pdf","creator":"dernst","file_size":790526,"date_updated":"2021-02-03T15:00:30Z","access_level":"open_access","checksum":"6f451f9c2b74bedbc30cf884a3e02670","content_type":"application/pdf","relation":"main_file","file_id":"9081","success":1,"date_created":"2021-02-03T15:00:30Z"}],"article_processing_charge":"Yes (via OA deal)","issue":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":381,"file_date_updated":"2021-02-03T15:00:30Z","oa":1,"publication_status":"published","author":[{"last_name":"Runkel","full_name":"Runkel, Ingo","first_name":"Ingo"},{"first_name":"Lorant","full_name":"Szegedy, Lorant","last_name":"Szegedy","id":"7943226E-220E-11EA-94C7-D59F3DDC885E","orcid":"0000-0003-2834-5054"}],"type":"journal_article","day":"01","title":"Area-dependent quantum field theory","citation":{"short":"I. Runkel, L. Szegedy, Communications in Mathematical Physics 381 (2021) 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>","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>.","ista":"Runkel I, Szegedy L. 2021. Area-dependent quantum field theory. Communications in Mathematical Physics. 381(1), 83–117.","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.","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>."},"ddc":["510"],"doi":"10.1007/s00220-020-03902-1","language":[{"iso":"eng"}],"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"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).","date_created":"2020-11-29T23:01:17Z","month":"01","page":"83–117","status":"public","intvolume":"       381","publication":"Communications in Mathematical Physics","quality_controlled":"1","department":[{"_id":"MiLe"}],"isi":1,"publisher":"Springer Nature"},{"language":[{"iso":"eng"}],"doi":"10.1007/s00220-020-03828-8","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.","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"day":"01","author":[{"first_name":"Nikita","full_name":"Kalinin, Nikita","last_name":"Kalinin"},{"id":"35084A62-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4310-178X","full_name":"Shkolnikov, Mikhail","first_name":"Mikhail","last_name":"Shkolnikov"}],"type":"journal_article","ec_funded":1,"citation":{"short":"N. Kalinin, M. Shkolnikov, Communications in Mathematical Physics 378 (2020) 1649–1675.","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>","ista":"Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. 378(9), 1649–1675.","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.","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>.","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>."},"title":"Sandpile solitons via smoothing of superharmonic functions","quality_controlled":"1","department":[{"_id":"TaHa"}],"publication":"Communications in Mathematical Physics","status":"public","intvolume":"       378","publisher":"Springer Nature","isi":1,"month":"09","date_created":"2020-08-30T22:01:13Z","page":"1649-1675","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2023-08-22T09:00:03Z","external_id":{"arxiv":["1711.04285"],"isi":["000560620600001"]},"scopus_import":"1","publication_identifier":{"issn":["00103616"],"eissn":["14320916"]},"article_type":"original","year":"2020","oa_version":"Preprint","volume":378,"publication_status":"published","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1711.04285","open_access":"1"}],"abstract":[{"lang":"eng","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. "}],"_id":"8325","date_published":"2020-09-01T00:00:00Z","arxiv":1,"issue":"9","article_processing_charge":"No"},{"citation":{"mla":"Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional II: The Dilute Limit.” <i>Communications in Mathematical Physics</i>, vol. 360, no. 1, Springer, 2018, pp. 347–403, doi:<a href=\"https://doi.org/10.1007/s00220-017-3064-x\">10.1007/s00220-017-3064-x</a>.","ista":"Napiórkowski MM, Reuvers R, Solovej J. 2018. The Bogoliubov free energy functional II: The dilute Limit. Communications in Mathematical Physics. 360(1), 347–403.","ieee":"M. M. Napiórkowski, R. Reuvers, and J. Solovej, “The Bogoliubov free energy functional II: The dilute Limit,” <i>Communications in Mathematical Physics</i>, vol. 360, no. 1. Springer, pp. 347–403, 2018.","chicago":"Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “The Bogoliubov Free Energy Functional II: The Dilute Limit.” <i>Communications in Mathematical Physics</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s00220-017-3064-x\">https://doi.org/10.1007/s00220-017-3064-x</a>.","apa":"Napiórkowski, M. M., Reuvers, R., &#38; Solovej, J. (2018). The Bogoliubov free energy functional II: The dilute Limit. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-017-3064-x\">https://doi.org/10.1007/s00220-017-3064-x</a>","ama":"Napiórkowski MM, Reuvers R, Solovej J. The Bogoliubov free energy functional II: The dilute Limit. <i>Communications in Mathematical Physics</i>. 2018;360(1):347-403. doi:<a href=\"https://doi.org/10.1007/s00220-017-3064-x\">10.1007/s00220-017-3064-x</a>","short":"M.M. Napiórkowski, R. Reuvers, J. Solovej, Communications in Mathematical Physics 360 (2018) 347–403."},"title":"The Bogoliubov free energy functional II: The dilute Limit","day":"01","type":"journal_article","author":[{"id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M","full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski"},{"full_name":"Reuvers, Robin","first_name":"Robin","last_name":"Reuvers"},{"full_name":"Solovej, Jan","first_name":"Jan","last_name":"Solovej"}],"project":[{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27"}],"language":[{"iso":"eng"}],"doi":"10.1007/s00220-017-3064-x","page":"347-403","month":"05","date_created":"2018-12-11T11:47:09Z","publisher":"Springer","quality_controlled":"1","department":[{"_id":"RoSe"}],"publication":"Communications in Mathematical Physics","intvolume":"       360","status":"public","publist_id":"7260","year":"2018","oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:02:35Z","external_id":{"arxiv":["1511.05953"]},"scopus_import":1,"publication_identifier":{"issn":["00103616"]},"arxiv":1,"issue":"1","_id":"554","date_published":"2018-05-01T00:00:00Z","abstract":[{"lang":"eng","text":"We analyse the canonical Bogoliubov free energy functional in three dimensions at low temperatures in the dilute limit. We prove existence of a first-order phase transition and, in the limit (Formula presented.), we determine the critical temperature to be (Formula presented.) to leading order. Here, (Formula presented.) is the critical temperature of the free Bose gas, ρ is the density of the gas and a is the scattering length of the pair-interaction potential V. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula in the limit (Formula presented.)."}],"publication_status":"published","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1511.05953","open_access":"1"}],"volume":360},{"project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}],"related_material":{"record":[{"id":"52","relation":"dissertation_contains","status":"public"}]},"doi":"10.1007/s00220-017-2980-0","ddc":["539"],"language":[{"iso":"eng"}],"title":"Stability of a fermionic N+1 particle system with point interactions","ec_funded":1,"citation":{"short":"T. Moser, R. Seiringer, Communications in Mathematical Physics 356 (2017) 329–355.","ama":"Moser T, Seiringer R. Stability of a fermionic N+1 particle system with point interactions. <i>Communications in Mathematical Physics</i>. 2017;356(1):329-355. doi:<a href=\"https://doi.org/10.1007/s00220-017-2980-0\">10.1007/s00220-017-2980-0</a>","apa":"Moser, T., &#38; Seiringer, R. (2017). Stability of a fermionic N+1 particle system with point interactions. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-017-2980-0\">https://doi.org/10.1007/s00220-017-2980-0</a>","chicago":"Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle System with Point Interactions.” <i>Communications in Mathematical Physics</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s00220-017-2980-0\">https://doi.org/10.1007/s00220-017-2980-0</a>.","ieee":"T. Moser and R. Seiringer, “Stability of a fermionic N+1 particle system with point interactions,” <i>Communications in Mathematical Physics</i>, vol. 356, no. 1. Springer, pp. 329–355, 2017.","ista":"Moser T, Seiringer R. 2017. Stability of a fermionic N+1 particle system with point interactions. Communications in Mathematical Physics. 356(1), 329–355.","mla":"Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle System with Point Interactions.” <i>Communications in Mathematical Physics</i>, vol. 356, no. 1, Springer, 2017, pp. 329–55, doi:<a href=\"https://doi.org/10.1007/s00220-017-2980-0\">10.1007/s00220-017-2980-0</a>."},"type":"journal_article","author":[{"id":"2B5FC9A4-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas","full_name":"Moser, Thomas","last_name":"Moser"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer"}],"day":"01","isi":1,"publisher":"Springer","intvolume":"       356","status":"public","quality_controlled":"1","department":[{"_id":"RoSe"}],"publication":"Communications in Mathematical Physics","page":"329 - 355","date_created":"2018-12-11T11:48:15Z","month":"11","publication_identifier":{"issn":["00103616"]},"date_updated":"2023-09-27T12:34:15Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000409821300010"]},"scopus_import":"1","oa_version":"Published Version","has_accepted_license":"1","year":"2017","publist_id":"6926","oa":1,"publication_status":"published","volume":356,"pubrep_id":"880","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"file_date_updated":"2020-07-14T12:47:57Z","issue":"1","article_processing_charge":"No","abstract":[{"text":"We prove that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m*. The value of m* is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain.","lang":"eng"}],"_id":"741","date_published":"2017-11-01T00:00:00Z","file":[{"file_name":"IST-2017-880-v1+1_s00220-017-2980-0.pdf","file_size":952639,"creator":"system","date_updated":"2020-07-14T12:47:57Z","access_level":"open_access","checksum":"0fd9435400f91e9b3c5346319a2d24e3","content_type":"application/pdf","file_id":"4841","relation":"main_file","date_created":"2018-12-12T10:10:50Z"}]},{"pubrep_id":"722","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":349,"file_date_updated":"2020-07-14T12:44:39Z","oa":1,"publication_status":"published","_id":"1207","abstract":[{"text":"The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.","lang":"eng"}],"date_published":"2017-02-01T00:00:00Z","file":[{"content_type":"application/pdf","relation":"main_file","file_id":"5102","date_created":"2018-12-12T10:14:47Z","file_name":"IST-2016-722-v1+1_s00220-016-2805-6.pdf","file_size":1033743,"creator":"system","checksum":"ddff79154c3daf27237de5383b1264a9","date_updated":"2020-07-14T12:44:39Z","access_level":"open_access"}],"article_processing_charge":"Yes (via OA deal)","issue":"3","publication_identifier":{"issn":["00103616"]},"external_id":{"isi":["000393696700005"]},"scopus_import":"1","date_updated":"2023-09-20T11:16:57Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","year":"2017","oa_version":"Published Version","has_accepted_license":"1","publist_id":"6141","intvolume":"       349","status":"public","publication":"Communications in Mathematical Physics","department":[{"_id":"LaEr"}],"quality_controlled":"1","isi":1,"publisher":"Springer","date_created":"2018-12-11T11:50:43Z","month":"02","page":"947 - 990","ddc":["530"],"doi":"10.1007/s00220-016-2805-6","language":[{"iso":"eng"}],"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"type":"journal_article","author":[{"full_name":"Bao, Zhigang","first_name":"Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"last_name":"Schnelli","full_name":"Schnelli, Kevin","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231"}],"day":"01","title":"Local law of addition of random matrices on optimal scale","citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition of Random Matrices on Optimal Scale.” <i>Communications in Mathematical Physics</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s00220-016-2805-6\">https://doi.org/10.1007/s00220-016-2805-6</a>.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” <i>Communications in Mathematical Physics</i>, vol. 349, no. 3. Springer, pp. 947–990, 2017.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 349(3), 947–990.","mla":"Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.” <i>Communications in Mathematical Physics</i>, vol. 349, no. 3, Springer, 2017, pp. 947–90, doi:<a href=\"https://doi.org/10.1007/s00220-016-2805-6\">10.1007/s00220-016-2805-6</a>.","short":"Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349 (2017) 947–990.","ama":"Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal scale. <i>Communications in Mathematical Physics</i>. 2017;349(3):947-990. doi:<a href=\"https://doi.org/10.1007/s00220-016-2805-6\">10.1007/s00220-016-2805-6</a>","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2017). Local law of addition of random matrices on optimal scale. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-016-2805-6\">https://doi.org/10.1007/s00220-016-2805-6</a>"},"ec_funded":1}]