{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T21:01:47Z","timestamp":1787864507594,"version":"build-2784847793"},"reference-count":45,"publisher":"American Physical Society (APS)","issue":"22","license":[{"start":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T00:00:00Z","timestamp":1764028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000271","name":"Science and Technology Facilities Council","doi-asserted-by":"publisher","award":["ST\/X000591\/1"],"award-info":[{"award-number":["ST\/X000591\/1"]}],"id":[{"id":"10.13039\/501100000271","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/Y028872\/1"],"award-info":[{"award-number":["EP\/Y028872\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2025,10,20]]},"abstract":"<jats:p>\n                    We numerically study\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mrow>\n                        <a:msub>\n                          <a:mrow>\n                            <a:mi mathvariant=\"double-struck\">Z<\/a:mi>\n                          <\/a:mrow>\n                          <a:mrow>\n                            <a:mi>N<\/a:mi>\n                          <\/a:mrow>\n                        <\/a:msub>\n                      <\/a:mrow>\n                    <\/a:math>\n                    lattice gauge theories in 4D as prototypical models of systems with\n                    <d:math xmlns:d=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <d:msub>\n                        <d:mi mathvariant=\"double-struck\">Z<\/d:mi>\n                        <d:mi>N<\/d:mi>\n                      <\/d:msub>\n                    <\/d:math>\n                    1-. For\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <g:mrow>\n                        <g:mi>N<\/g:mi>\n                        <g:mo>\u2265<\/g:mo>\n                        <g:mn>3<\/g:mn>\n                      <\/g:mrow>\n                    <\/g:math>\n                    , we provide evidence that such systems exhibit not only the expected phases with spontaneously broken\/restored symmetry but also a third photon phase. When present, the 1-form symmetry provides a precise notion of confinement, and it is commonly believed that confinement ensues due to the proliferation of extended, stringlike objects known as , which carry a\n                    <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <i:msub>\n                        <i:mi mathvariant=\"double-struck\">Z<\/i:mi>\n                        <i:mi>N<\/i:mi>\n                      <\/i:msub>\n                    <\/i:math>\n                    flux. However, this picture is challenged by the three-phase scenario investigated here. We show that both the confined and the photon phases are associated with the proliferation of center vortices and that the key difference between them lies in whether or not vortex junctions\u2014the  proliferate.\n                  <\/jats:p>","DOI":"10.1103\/h8mn-t4fk","type":"journal-article","created":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T13:00:11Z","timestamp":1764075611000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Emergent Photons and Confinement: A Numerical Study on\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <mml:mrow>\n                        <mml:msub>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"double-struck\">Z<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:mi>N<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    Lattice Gauge Theory"],"prefix":"10.1103","volume":"135","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4252-0058","authenticated-orcid":true,"given":"Jeffrey","family":"Giansiracusa","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01v29qb04","id-type":"ROR","asserted-by":"publisher"}],"name":"Durham University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-5030-2668","authenticated-orcid":true,"given":"David","family":"Lanners","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01v29qb04","id-type":"ROR","asserted-by":"publisher"}],"name":"Durham University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6671-4060","authenticated-orcid":true,"given":"Tin","family":"Sulejmanpasic","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01v29qb04","id-type":"ROR","asserted-by":"publisher"}],"name":"Durham University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,11,25]]},"reference":[{"key":"h8mn-t4fkCc1R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP04(2014)001","type":"journal-article"},{"key":"h8mn-t4fkCc2R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP02(2015)172","type":"journal-article"},{"key":"h8mn-t4fkCc3R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP05(2017)091","type":"journal-article"},{"key":"h8mn-t4fkCc4R1","unstructured":"The 1-form symmetries were known in SU(N) Yang-Mills theory at least since the late 70\u00a0s [5], but until recently were relatively poorly understood.","type":"other"},{"key":"h8mn-t4fkCc5R1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(78)90737-2","type":"journal-article"},{"key":"h8mn-t4fkCc6R1","doi-asserted-by":"publisher","DOI":"10.21468\/SciPostPhys.6.1.006","type":"journal-article"},{"key":"h8mn-t4fkCc7R1","doi-asserted-by":"publisher","DOI":"10.21468\/SciPostPhys.13.5.114","type":"journal-article"},{"key":"h8mn-t4fkCc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.134.141902","type":"journal-article"},{"key":"h8mn-t4fkCc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.19.3698","type":"journal-article"},{"key":"h8mn-t4fkCc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.20.1915","type":"journal-article"},{"key":"h8mn-t4fkCc11R1","volume-title":"Lect. Notes Phys.","author":"J. Greensite","year":"2020","type":"book"},{"key":"h8mn-t4fkCc12R1","doi-asserted-by":"publisher","DOI":"10.1051\/epjconf\/201713701009","type":"journal-article"},{"key":"h8mn-t4fkCc13R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(80)90435-6","type":"journal-article"},{"key":"h8mn-t4fkCc14R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/h8mn-t4fk for details on computations and the order of the phase transition. It includes Refs.\u00a0[15\u201321].","type":"other"},{"key":"h8mn-t4fkCc15R1","unstructured":"W. Janke, Statistical analysis of simulations: Data correlations and error estimation, in Quantum simulations of complex many-body systems: From theory to algorithms vol.\u00a010, p.\u00a0423 (2002).","type":"other"},{"key":"h8mn-t4fkCc16R1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(79)90098-8","type":"journal-article"},{"key":"h8mn-t4fkCc17R1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-conmatphys-040721-021029","type":"journal-article"},{"key":"h8mn-t4fkCc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.125013","type":"journal-article"},{"key":"h8mn-t4fkCc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.108.195147","type":"journal-article"},{"key":"h8mn-t4fkCc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.7.1888","type":"journal-article"},{"key":"h8mn-t4fkCc21R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP06(2022)149","type":"journal-article"},{"key":"h8mn-t4fkCc22R1","volume-title":"The Millennium Prize Problems","author":"A. Jaffe","year":"2006","type":"book"},{"key":"h8mn-t4fkCc23R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(77)90086-4","type":"journal-article"},{"key":"h8mn-t4fkCc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.80.065001","type":"journal-article"},{"key":"h8mn-t4fkCc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.78.065035","type":"journal-article"},{"key":"h8mn-t4fkCc26R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP10(2012)115","type":"journal-article"},{"key":"h8mn-t4fkCc27R1","unstructured":"We note that by convention s\u2212\u2113=\u2212s\u2113\u2009\u2009mod\u2009\u2009N.","type":"other"},{"key":"h8mn-t4fkCc28R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(78)90153-0","type":"journal-article"},{"key":"h8mn-t4fkCc29R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(79)90111-1","type":"journal-article"},{"key":"h8mn-t4fkCc30R1","volume-title":"Algebraic Topology: Homology and Cohomology","author":"A.\u2009H. Wallace","year":"1970","type":"book"},{"key":"h8mn-t4fkCc31R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2019.114616","type":"journal-article"},{"key":"h8mn-t4fkCc32R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.27.938","type":"journal-article"},{"key":"h8mn-t4fkCc33R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(83)90220-1","type":"journal-article"},{"key":"h8mn-t4fkCc34R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(83)90217-1","type":"journal-article"},{"key":"h8mn-t4fkCc35R1","unstructured":"One way is to note that \u27e8A\u03bc(x)A\u03bd(y)\u27e9=\u03b4\u03bc\u03bd\/|x\u2212y|2 in the Feynman gauge, and then take derivatives.","type":"other"},{"key":"h8mn-t4fkCc36R1","unstructured":"The combination is chosen because, by reflection positivity, it is a sum of positive definite parts.","type":"other"},{"key":"h8mn-t4fkCc37R1","unstructured":"Defining monopoles and center vortices requires gauge fixing in SU(N) gauge theories (see, e.g., Refs.\u00a0[11, 12, 38]), although there are some efforts to identify such objects without it [39]. Further, a novel proposal of how to discretize SU(N) gauge theories [40, 41], may be related to a gauge invariant definition of vortices and monopoles [42].","type":"other"},{"key":"h8mn-t4fkCc38R1","volume-title":"NATO Advanced Study Institute on Confinement, Duality and Nonperturbative Aspects of QCD","author":"M.\u2009N. Chernodub","year":"1997","type":"conference-proceedings"},{"key":"h8mn-t4fkCc39R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.107.034501","type":"journal-article"},{"key":"h8mn-t4fkCc40R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP06(2025)085","type":"journal-article"},{"key":"h8mn-t4fkCc42R1","unstructured":"J.-Y. Chen (private Communications).","type":"other"},{"key":"h8mn-t4fkCc43R1","unstructured":"T.\u2009S. would like to thank M. Nguyen and E. Richards for discussions on this point.","type":"other"},{"key":"h8mn-t4fkCc44R1","unstructured":"The lattice simulations of DN seem to indicate three phases for N\u22736 [45].","type":"other"},{"key":"h8mn-t4fkCc45R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.105.114501","type":"journal-article"},{"key":"h8mn-t4fkCc46R1","unstructured":"J. Giansiracusa, D. Lanners, and T. Sulejmanpasic, Data for: Emergent photons and confinement: A numerical study on Zn lattice gauge theory, zenodo, 10.5281\/zenodo.17467336 (2025).","type":"other"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/h8mn-t4fk","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/h8mn-t4fk\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T13:00:29Z","timestamp":1764075629000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/h8mn-t4fk"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,25]]},"references-count":45,"journal-issue":{"issue":"22","published-print":{"date-parts":[[2025,11]]}},"URL":"https:\/\/doi.org\/10.1103\/h8mn-t4fk","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2505.00079","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,25]]},"assertion":[{"value":"2025-07-10","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"221901"}}