{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T15:26:51Z","timestamp":1758814011287,"version":"3.37.3"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T00:00:00Z","timestamp":1656633600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T00:00:00Z","timestamp":1658102400000},"content-version":"vor","delay-in-days":17,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. High Energ. Phys."],"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n                     <\/jats:title><jats:p>We study a generalization of 4-dimensional <jats:italic>BF<\/jats:italic>-theory in the context of higher gauge theory. We construct a triangulation independent topological state sum <jats:italic>Z<\/jats:italic>, based on the classical 3<jats:italic>BF<\/jats:italic> action for a general 3-group and a 4-dimensional spacetime manifold <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \\mathcal{M} $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>M<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula><jats:sub>4<\/jats:sub>. This state sum coincides with Porter\u2019s TQFT for <jats:italic>d<\/jats:italic> = 4 and <jats:italic>n<\/jats:italic> = 3. In order to verify that the constructed state sum is a topological invariant of the underlying 4-dimensional manifold, its behavior under Pachner moves is analyzed, and it is obtained that the state sum <jats:italic>Z<\/jats:italic> remains the same. This paper is a generalization of the work done by Girelli, Pfeiffer, and Popescu for the case of state sum based on the classical 2<jats:italic>BF<\/jats:italic> action with the underlying 2-group structure.<\/jats:p>","DOI":"10.1007\/jhep07(2022)105","type":"journal-article","created":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T05:02:37Z","timestamp":1658206957000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Topological invariant of 4-manifolds based on a 3-group"],"prefix":"10.1007","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2310-5281","authenticated-orcid":false,"given":"T.","family":"Radenkovi\u0107","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6977-4870","authenticated-orcid":false,"given":"M.","family":"Vojinovi\u0107","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,7,18]]},"reference":[{"key":"18754_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755804","volume-title":"Quantum Gravity","author":"C Rovelli","year":"2004","unstructured":"C. Rovelli, Quantum Gravity, Cambridge University Press, Cambridge, U.K. (2004)."},{"key":"18754_CR2","unstructured":"C. Rovelli, Zakopane lectures on loop gravity, PoS QGQGS2011 (2011) 003 [arXiv:1102.3660] [INSPIRE]."},{"key":"18754_CR3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755682","volume-title":"Modern Canonical Quantum General Relativity","author":"T Thiemann","year":"2007","unstructured":"T. Thiemann, Modern Canonical Quantum General Relativity, Cambridge University Press, Cambridge, U.K. (2007)."},{"key":"18754_CR4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107706910","volume-title":"Covariant Loop Quantum Gravity","author":"C Rovelli","year":"2014","unstructured":"C. Rovelli and F. Vidotto, Covariant Loop Quantum Gravity, Cambridge University Press, Cambridge, U.K. (2014)."},{"key":"18754_CR5","doi-asserted-by":"crossref","unstructured":"J.F. Plebanski, On the separation of Einsteinian substructures, J. Math. Phys. 18 (1977) 2511 [INSPIRE].","DOI":"10.1063\/1.523215"},{"key":"18754_CR6","unstructured":"G. Ponzano and T. Regge, Spectroscopic and Group Theoretical Methods in Physics. Racah Memorial Volume, North-Holland, Amsterdam, Netherlands (1968) pp. 75\u2013103."},{"key":"18754_CR7","doi-asserted-by":"crossref","unstructured":"J.W. Barrett and L. Crane, Relativistic spin networks and quantum gravity, J. Math. Phys. 39 (1998) 3296 [gr-qc\/9709028] [INSPIRE].","DOI":"10.1063\/1.532254"},{"key":"18754_CR8","doi-asserted-by":"crossref","unstructured":"J.W. Barrett and L. Crane, A Lorentzian signature model for quantum general relativity, Class. Quant. Grav. 17 (2000) 3101 [gr-qc\/9904025] [INSPIRE].","DOI":"10.1088\/0264-9381\/17\/16\/302"},{"key":"18754_CR9","doi-asserted-by":"publisher","first-page":"2799","DOI":"10.1142\/S0217732392004171","volume":"7","author":"H Ooguri","year":"1992","unstructured":"H. Ooguri, Topological lattice models in four-dimensions, Mod. Phys. Lett. A 7 (1992) 2799 [hep-th\/9205090] [INSPIRE].","journal-title":"Mod. Phys. Lett. A"},{"key":"18754_CR10","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1016\/j.nuclphysb.2008.02.018","volume":"799","author":"J Engle","year":"2008","unstructured":"J. Engle, E. Livine, R. Pereira and C. Rovelli, LQG vertex with finite Immirzi parameter, Nucl. Phys. B 799 (2008) 136 [arXiv:0711.0146] [INSPIRE].","journal-title":"Nucl. Phys. B"},{"key":"18754_CR11","doi-asserted-by":"crossref","unstructured":"L. Freidel and K. Krasnov, A New Spin Foam Model for 4d Gravity, Class. Quant. Grav. 25 (2008) 125018 [arXiv:0708.1595] [INSPIRE].","DOI":"10.1088\/0264-9381\/25\/12\/125018"},{"key":"18754_CR12","doi-asserted-by":"crossref","unstructured":"A. Mikovi\u0107 and M. Vojinovi\u0107, Effective action for EPRL\/FK spin foam models, J. Phys. Conf. Ser. 360 (2012) 012049 [arXiv:1110.6114] [INSPIRE].","DOI":"10.1088\/1742-6596\/360\/1\/012049"},{"key":"18754_CR13","doi-asserted-by":"crossref","unstructured":"A. Mikovi\u0107 and M. Vojinovi\u0107, A finiteness bound for the EPRL\/FK spin foam model, Class. Quant. Grav. 30 (2013) 035001 [arXiv:1101.3294] [INSPIRE].","DOI":"10.1088\/0264-9381\/30\/3\/035001"},{"key":"18754_CR14","doi-asserted-by":"publisher","first-page":"40008","DOI":"10.1209\/0295-5075\/110\/40008","volume":"110","author":"A Mikovi\u0107","year":"2015","unstructured":"A. Mikovi\u0107 and M. Vojinovi\u0107, Solution to the Cosmological Constant Problem in a Regge Quantum Gravity Model, EPL 110 (2015) 40008 [arXiv:1407.1394] [INSPIRE].","journal-title":"EPL"},{"key":"18754_CR15","doi-asserted-by":"crossref","unstructured":"E. Bianchi, M. Han, C. Rovelli, W. Wieland, E. Magliaro and C. Perini, Spinfoam fermions, Class. Quant. Grav. 30 (2013) 235023 [arXiv:1012.4719] [INSPIRE].","DOI":"10.1088\/0264-9381\/30\/23\/235023"},{"key":"18754_CR16","doi-asserted-by":"publisher","first-page":"2335","DOI":"10.1007\/s10714-010-1070-9","volume":"43","author":"JC Baez","year":"2011","unstructured":"J.C. Baez and J. Huerta, An Invitation to Higher Gauge Theory, Gen. Rel. Grav. 43 (2011) 2335 [arXiv:1003.4485] [INSPIRE].","journal-title":"Gen. Rel. Grav."},{"key":"18754_CR17","unstructured":"Z. Li, A Global Geometric Approach to Parallel Transport of Strings in Gauge Theory, arXiv:1910.14230 [INSPIRE]."},{"key":"18754_CR18","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/s00220-014-2022-0","volume":"328","author":"C S\u00e4mann","year":"2014","unstructured":"C. S\u00e4mann and M. Wolf, Non-Abelian Tensor Multiplet Equations from Twistor Space, Commun. Math. Phys. 328 (2014) 527 [arXiv:1205.3108] [INSPIRE].","journal-title":"Commun. Math. Phys."},{"key":"18754_CR19","doi-asserted-by":"publisher","first-page":"087","DOI":"10.1007\/JHEP04(2015)087","volume":"04","author":"B Jur\u010do","year":"2015","unstructured":"B. Jur\u010do, C. S\u00e4mann and M. Wolf, Semistrict Higher Gauge Theory, JHEP 04 (2015) 087 [arXiv:1403.7185] [INSPIRE].","journal-title":"JHEP"},{"key":"18754_CR20","doi-asserted-by":"crossref","unstructured":"Y. Hidaka, M. Nitta and R. Yokokura, Higher-form symmetries and 3-group in axion electrodynamics, Phys. Lett. B 808 (2020) 135672 [arXiv:2006.12532] [INSPIRE].","DOI":"10.1016\/j.physletb.2020.135672"},{"key":"18754_CR21","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/JHEP01(2021)173","volume":"01","author":"Y Hidaka","year":"2021","unstructured":"Y. Hidaka, M. Nitta and R. Yokokura, Global 3-group symmetry and \u2019t Hooft anomalies in axion electrodynamics, JHEP 01 (2021) 173 [arXiv:2009.14368] [INSPIRE].","journal-title":"JHEP"},{"key":"18754_CR22","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.1007\/s11005-014-0704-3","volume":"104","author":"C S\u00e4emann","year":"2014","unstructured":"C. S\u00e4emann and M. Wolf, Six-Dimensional Superconformal Field Theories from Principal 3-Bundles over Twistor Space, Lett. Math. Phys. 104 (2014) 1147 [arXiv:1305.4870] [INSPIRE].","journal-title":"Lett. Math. Phys."},{"key":"18754_CR23","doi-asserted-by":"crossref","unstructured":"D. Song, K. Lou, K. Wu, J. Yang and F. Zhang, 3-form Yang-Mills based on 2-crossed modules, J. Geom. Phys. 178 (2022) 104537 [arXiv:2108.12852] [INSPIRE].","DOI":"10.1016\/j.geomphys.2022.104537"},{"key":"18754_CR24","unstructured":"D. Song, K. Lou, K. Wu and J. Yang, Higher form Yang-Mills as higher BFYM theories, arXiv:2109.13443 [INSPIRE]."},{"key":"18754_CR25","doi-asserted-by":"crossref","unstructured":"Y. Hidaka, M. Nitta and R. Yokokura, Topological axion electrodynamics and 4-group symmetry, Phys. Lett. B 823 (2021) 136762 [arXiv:2107.08753] [INSPIRE].","DOI":"10.1016\/j.physletb.2021.136762"},{"key":"18754_CR26","first-page":"04A109","volume":"2022","author":"Y Hidaka","year":"2022","unstructured":"Y. Hidaka, M. Nitta and R. Yokokura, Global 4-group symmetry and \u2019t Hooft anomalies in topological axion electrodynamics, PTEP 2022 (2022) 04A109 [arXiv:2108.12564] [INSPIRE].","journal-title":"PTEP"},{"key":"18754_CR27","doi-asserted-by":"publisher","first-page":"674","DOI":"10.1002\/prop.201600031","volume":"64","author":"B Jur\u010do","year":"2016","unstructured":"B. Jur\u010do, C. S\u00e4mann and M. Wolf, Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations, Fortsch. Phys. 64 (2016) 674 [arXiv:1604.01639] [INSPIRE].","journal-title":"Fortsch. Phys."},{"key":"18754_CR28","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/JHEP07(2017)111","volume":"07","author":"C S\u00e4mann","year":"2017","unstructured":"C. S\u00e4mann and M. Wolf, Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory, JHEP 07 (2017) 111 [arXiv:1702.04160] [INSPIRE].","journal-title":"JHEP"},{"key":"18754_CR29","doi-asserted-by":"publisher","first-page":"1910025","DOI":"10.1002\/prop.201910025","volume":"67","author":"B Jur\u010do","year":"2019","unstructured":"B. Jur\u010do, T. Macrelli, L. Raspollini, C. S\u00e4mann and M. Wolf, L\u221e-Algebras, the BV Formalism, and Classical Fields, Fortsch. Phys. 67 (2019) 1910025 [arXiv:1903.02887] [INSPIRE].","journal-title":"Fortsch. Phys."},{"key":"18754_CR30","doi-asserted-by":"crossref","unstructured":"A. Mikovi\u0107 and M. Vojinovi\u0107, Poincar\u00e9 2-group and quantum gravity, Class. Quant. Grav. 29 (2012) 165003 [arXiv:1110.4694] [INSPIRE].","DOI":"10.1088\/0264-9381\/29\/16\/165003"},{"key":"18754_CR31","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1007\/JHEP10(2019)222","volume":"10","author":"T Radenkovi\u0107","year":"2019","unstructured":"T. Radenkovi\u0107 and M. Vojinovi\u0107, Higher Gauge Theories Based on 3-groups, JHEP 10 (2019) 222 [arXiv:1904.07566] [INSPIRE].","journal-title":"JHEP"},{"key":"18754_CR32","doi-asserted-by":"publisher","first-page":"61001","DOI":"10.1209\/0295-5075\/133\/61001","volume":"133","author":"A Mikovi\u0107","year":"2021","unstructured":"A. Mikovi\u0107 and M. Vojinovi\u0107, Standard Model and 4-groups, EPL 133 (2021) 61001 [arXiv:2008.06354] [INSPIRE].","journal-title":"EPL"},{"key":"18754_CR33","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1112\/S0024610798006838","volume":"58","author":"T Porter","year":"1998","unstructured":"T. Porter, Topological quantum field theories from homotopy n-types, J. London Math. Soc. 58 (1998) 723.","journal-title":"J. London Math. Soc."},{"key":"18754_CR34","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1142\/S0218216596000400","volume":"5","author":"T Porter","year":"1996","unstructured":"T. Porter, Interpretations of Yetter\u2019s notion of G-coloring: simplicial fibre bundles and non-abelian cohomology, J. Knot Th. Ramif. 5 (1996) 687.","journal-title":"J. Knot Th. Ramif."},{"key":"18754_CR35","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/S0195-6698(13)80080-7","volume":"12","author":"U Pachner","year":"1991","unstructured":"U. Pachner, PL homeomorphic manifolds are equivalent by elementary shellings, Europ. J. Combinat. 12 (1991) 129 [arXiv:1095161].","journal-title":"Europ. J. Combinat."},{"key":"18754_CR36","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/33\/21\/213001","volume":"33","author":"M Celada","year":"2016","unstructured":"M. Celada, D. Gonz\u00e1lez and M. Montesinos, BF gravity, Class. Quant. Grav. 33 (2016) 213001 [arXiv:1610.02020] [INSPIRE].","journal-title":"Class. Quant. Grav."},{"key":"18754_CR37","doi-asserted-by":"crossref","unstructured":"J.C. Baez, An Introduction to Spin Foam Models of BF Theory and Quantum Gravity, Lect. Notes Phys. 543 (2000) 25 [gr-qc\/9905087] [INSPIRE].","DOI":"10.1007\/3-540-46552-9_2"},{"key":"18754_CR38","doi-asserted-by":"crossref","unstructured":"F. Girelli, H. Pfeiffer and E.M. Popescu, Topological Higher Gauge Theory - from BF to BFCG theory, J. Math. Phys. 49 (2008) 032503 [arXiv:0708.3051] [INSPIRE].","DOI":"10.1063\/1.2888764"},{"key":"18754_CR39","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.4310\/ATMP.2011.v15.n4.a4","volume":"15","author":"JF Martins","year":"2011","unstructured":"J.F. Martins and A. Mikovi\u0107, Lie crossed modules and gauge-invariant actions for 2-BF theories, Adv. Theor. Math. Phys. 15 (2011) 1059 [arXiv:1006.0903] [INSPIRE].","journal-title":"Adv. Theor. Math. Phys."},{"key":"18754_CR40","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1007\/s10714-015-1900-x","volume":"47","author":"A Mikovi\u0107","year":"2015","unstructured":"A. Mikovi\u0107 and M.A. Oliveira, Canonical formulation of Poincar\u00e9 BFCG theory and its quantization, Gen. Rel. Grav. 47 (2015) 58 [arXiv:1409.3751] [INSPIRE].","journal-title":"Gen. Rel. Grav."},{"key":"18754_CR41","unstructured":"A. Mikovi\u0107, M.A. Oliveira and M. Vojinovi\u0107, Hamiltonian analysis of the BFCG theory for a strict Lie 2-group, arXiv:1610.09621 [INSPIRE]."},{"key":"18754_CR42","unstructured":"J.F. Martins and R. Picken, The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module, arXiv:0907.2566 [INSPIRE]."},{"key":"18754_CR43","doi-asserted-by":"crossref","unstructured":"W. Wang, On 3-gauge transformations, 3-curvatures, and Gray-categories, J. Math. Phys. 55 (2014) 043506 [arXiv:1311.3796] [INSPIRE].","DOI":"10.1063\/1.4870640"},{"key":"18754_CR44","doi-asserted-by":"publisher","first-page":"620","DOI":"10.3390\/sym12040620","volume":"12","author":"T Radenkovi\u0107","year":"2020","unstructured":"T. Radenkovi\u0107 and M. Vojinovi\u0107, Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory, Symmetry 12 (2020) 620 [arXiv:2004.06901] [INSPIRE].","journal-title":"Symmetry"},{"key":"18754_CR45","doi-asserted-by":"crossref","unstructured":"T. Radenkovi\u0107 and M. Vojinovi\u0107, Gauge symmetry of the 3BF theory for a generic semistrict Lie three-group, Class. Quant. Grav. 39 (2022) 135009 [arXiv:2101.04049] [INSPIRE].","DOI":"10.1088\/1361-6382\/ac6b78"},{"key":"18754_CR46","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/0022-4049(84)90034-3","volume":"34","author":"D Conduch\u00e9","year":"1984","unstructured":"D. Conduch\u00e9, Modules crois\u00e9s g\u00e9n\u00e9ralis\u00e9s de longueur 2, in proceedings of the Luminy conference on algebraic K-theory (Luminy, 1983), J. Pure Appl. Algebra 34, (1984) 155.","journal-title":"J. Pure Appl. Algebra"},{"key":"18754_CR47","doi-asserted-by":"publisher","first-page":"3949","DOI":"10.1063\/1.1790048","volume":"45","author":"F Girelli","year":"2004","unstructured":"F. Girelli and H. Pfeiffer, Higher gauge theory: Differential versus integral formulation, J. Math. Phys. 45 (2004) 3949 [hep-th\/0309173] [INSPIRE].","journal-title":"J. Math. Phys."},{"key":"18754_CR48","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S0218216592000021","volume":"1","author":"DN Yetter","year":"1992","unstructured":"D.N. Yetter, Topological quantum field theories associated to finite groups and crossed G-sets, J. Knot Theory Ramifications 1 (1992) 1.","journal-title":"J. Knot Theory Ramifications"},{"key":"18754_CR49","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1142\/S0218216593000076","volume":"2","author":"DN Yetter","year":"1993","unstructured":"D.N. Yetter, TQFT\u2019s from homotopy 2-types, J. Knot Theory Ramifications 2 (1993) 113.","journal-title":"J. Knot Theory Ramifications"},{"key":"18754_CR50","doi-asserted-by":"crossref","unstructured":"A. Baratin and L. Freidel, A 2-categorical state sum model, J. Math. Phys. 56 (2015) 011705 [arXiv:1409.3526] [INSPIRE].","DOI":"10.1063\/1.4906369"},{"key":"18754_CR51","doi-asserted-by":"crossref","unstructured":"S.K. Asante, B. Dittrich, F. Girelli, A. Riello and P. Tsimiklis, Quantum geometry from higher gauge theory, Class. Quant. Grav. 37 (2020) 205001 [arXiv:1908.05970] [INSPIRE].","DOI":"10.1088\/1361-6382\/aba589"},{"key":"18754_CR52","unstructured":"F. Girelli, M. Laudonio and P. Tsimiklis, Polyhedron phase space using 2-groups: \u03ba-Poincar\u00e9 as a Poisson 2-group, arXiv:2105.10616 [INSPIRE]."}],"container-title":["Journal of High Energy Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP07(2022)105.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/JHEP07(2022)105\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP07(2022)105.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T05:20:42Z","timestamp":1658208042000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/JHEP07(2022)105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7]]},"references-count":52,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["18754"],"URL":"https:\/\/doi.org\/10.1007\/jhep07(2022)105","relation":{},"ISSN":["1029-8479"],"issn-type":[{"type":"electronic","value":"1029-8479"}],"subject":[],"published":{"date-parts":[[2022,7]]},"assertion":[{"value":"17 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 July 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"105"}}