{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T11:26:15Z","timestamp":1772796375139,"version":"3.50.1"},"reference-count":71,"publisher":"American Physical Society (APS)","issue":"9","license":[{"start":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T00:00:00Z","timestamp":1764115200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100031060","name":"European High Performance Computing Joint Undertaking","doi-asserted-by":"publisher","award":["101101903"],"award-info":[{"award-number":["101101903"]}],"id":[{"id":"10.13039\/100031060","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04540"],"award-info":[{"award-number":["UIDB\/04540"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"CEFEMA","award":["UIDB\/04540\/2020"],"award-info":[{"award-number":["UIDB\/04540\/2020"]}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. D"],"accepted":{"date-parts":[[2025,11,7]]},"abstract":"<jats:p>\n                    In this study, we conduct a thorough examination of the spectrum of the open confining string in\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mrow>\n                        <a:mn>3<\/a:mn>\n                        <a:mo>+<\/a:mo>\n                        <a:mn>1<\/a:mn>\n                      <\/a:mrow>\n                    <\/a:math>\n                    dimensions, commonly referred to as the open flux tube, across various gauge groups of\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <c:mi>S<\/c:mi>\n                      <c:mi>U<\/c:mi>\n                      <c:mo stretchy=\"false\">(<\/c:mo>\n                      <c:msub>\n                        <c:mi>N<\/c:mi>\n                        <c:mi>c<\/c:mi>\n                      <\/c:msub>\n                      <c:mo stretchy=\"false\">)<\/c:mo>\n                    <\/c:math>\n                    . Our primary objective is to explore its behavior as we approach the large-\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <g:msub>\n                        <g:mi>N<\/g:mi>\n                        <g:mi>c<\/g:mi>\n                      <\/g:msub>\n                    <\/g:math>\n                    limit and the identification of possible world-sheet axion states. Specifically, we undertake a detailed analysis of the associated spectrum for\n                    <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <i:msub>\n                        <i:mi>N<\/i:mi>\n                        <i:mi>c<\/i:mi>\n                      <\/i:msub>\n                      <i:mo>=<\/i:mo>\n                      <i:mn>3<\/i:mn>\n                    <\/i:math>\n                    , 4, 5, 6. This marks the first systematic investigation of the open flux-tube spectrum within the context of the large-\n                    <k:math xmlns:k=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <k:msub>\n                        <k:mi>N<\/k:mi>\n                        <k:mi>c<\/k:mi>\n                      <\/k:msub>\n                    <\/k:math>\n                    limit. More specifically, we analyze the spectra of flux tubes that form between a static quark-antiquark pair, considering a significant number of radial excitations and eight irreducible representations characterized by the quantum numbers of angular momentum\n                    <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <m:mi mathvariant=\"normal\">\u039b<\/m:mi>\n                    <\/m:math>\n                    , charge conjugation and parity\n                    <p:math xmlns:p=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <p:msub>\n                        <p:mi>\u03b7<\/p:mi>\n                        <p:mrow>\n                          <p:mi>C<\/p:mi>\n                          <p:mi>P<\/p:mi>\n                        <\/p:mrow>\n                      <\/p:msub>\n                    <\/p:math>\n                    , and the reflection symmetry\n                    <r:math xmlns:r=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <r:mi>\u03b5<\/r:mi>\n                    <\/r:math>\n                    for\n                    <t:math xmlns:t=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <t:mi mathvariant=\"normal\">\u039b<\/t:mi>\n                      <t:mo>=<\/t:mo>\n                      <t:mn>0<\/t:mn>\n                    <\/t:math>\n                    . To this purpose we employ a diverse set of suitable operators, an anisotropic action, and smearing techniques, and solve the generalized eigenvalue problem. We compare our findings with predictions from the Nambu-Goto string model to assess potential tensions indicative of novel phenomena such as the existence of axionlike state along the flux-tube world sheet. Notably, we provide undoubted evidence of the existence of a massive axionlike particle with the same mass as the corresponding axion extracted within the context of closed flux tube. This strengthens the conjecture that the axion is a property of the world sheet of the QCD string.\n                  <\/jats:p>","DOI":"10.1103\/2g74-q38h","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T05:08:20Z","timestamp":1762492100000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Spectrum of open confining strings in the large-\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <mml:msub>\n                        <mml:mi>N<\/mml:mi>\n                        <mml:mi>c<\/mml:mi>\n                      <\/mml:msub>\n                    <\/mml:math>\n                    limit"],"prefix":"10.1103","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2021-0614","authenticated-orcid":true,"given":"Alireza","family":"Sharifian","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Instituto Superior T\u00e9cnico (Universidade de Lisboa)"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4600-4245","authenticated-orcid":true,"given":"Andreas","family":"Athenodorou","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01q8k8p90","id-type":"ROR","asserted-by":"publisher"}],"name":"The Cyprus Institute"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1556-0580","authenticated-orcid":true,"given":"Pedro","family":"Bicudo","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Instituto Superior T\u00e9cnico (Universidade de Lisboa)"}]}],"member":"16","published-online":{"date-parts":[[2025,11,26]]},"reference":[{"key":"2g74-q38hCc1R1","unstructured":"Simons Collaboration on Confinement and QCD Strings, https:\/\/simonsconfinementcollaboration.org\/.","type":"other"},{"key":"2g74-q38hCc2R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2007.09.045","type":"journal-article"},{"key":"2g74-q38hCc3R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP02(2011)030","type":"journal-article"},{"key":"2g74-q38hCc4R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP05(2011)042","type":"journal-article"},{"key":"2g74-q38hCc6R1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(79)91193-6","type":"journal-article"},{"key":"2g74-q38hCc7R1","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.46.1560","type":"journal-article"},{"key":"2g74-q38hCc8R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511841682","type":"book","volume-title":"A First Course in String Theory","author":"B. 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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":"094517"}}