{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T22:00:17Z","timestamp":1771020017250,"version":"3.50.1"},"reference-count":62,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2018,9,1]],"date-time":"2018-09-01T00:00:00Z","timestamp":1535760000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2018,9,7]],"date-time":"2018-09-07T00:00:00Z","timestamp":1536278400000},"content-version":"vor","delay-in-days":6,"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":[[2018,9]]},"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc><\/jats:title><jats:p>We construct a new class of differential operators that naturally act on AdS harmonic functions. These are weight shifting operators that change the spin and dimension of AdS representations. Together with CFT weight shifting operators, the new operators obey crossing equations that relate distinct representations of the conformal group. We apply our findings to the computation of Witten diagrams, focusing on the particular case of cubic interactions and on massive, symmetric and traceless fields. In particular we show that tree level 4-point Witten diagrams with arbitrary spins, both in the external fields and in the exchanged field, can be reduced to the action of weight shifting operators on similar 4-point Witten diagrams where all fields are scalars. We also show how to obtain the conformal partial wave expansion of these diagrams using the new set of operators. In the case of 1-loop diagrams with cubic couplings we show how to reduce them to similar 1-loop diagrams with scalar fields except for a single external spinning field (which must be a scalar in the case of a two-point diagram). As a bonus, we provide new CFT and AdS weight shifting operators for mixed-symmetry tensors.<\/jats:p>","DOI":"10.1007\/jhep09(2018)040","type":"journal-article","created":{"date-parts":[[2018,9,8]],"date-time":"2018-09-08T14:18:08Z","timestamp":1536416288000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":44,"title":["AdS weight shifting operators"],"prefix":"10.1007","volume":"2018","author":[{"given":"Miguel S.","family":"Costa","sequence":"first","affiliation":[]},{"given":"Tobias","family":"Hansen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,9,7]]},"reference":[{"key":"8968_CR1","doi-asserted-by":"crossref","unstructured":"J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th\/9711200] [INSPIRE].","DOI":"10.1063\/1.59653"},{"key":"8968_CR2","doi-asserted-by":"crossref","unstructured":"E.S. Fradkin and M.A. Vasiliev, On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].","DOI":"10.1016\/0370-2693(87)91275-5"},{"key":"8968_CR3","doi-asserted-by":"crossref","unstructured":"M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3+1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].","DOI":"10.1016\/0370-2693(90)91400-6"},{"key":"8968_CR4","doi-asserted-by":"crossref","unstructured":"I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th\/0210114] [INSPIRE].","DOI":"10.1016\/S0370-2693(02)02980-5"},{"key":"8968_CR5","unstructured":"V.E. Didenko and E.D. Skvortsov, Elements of Vasiliev theory, arXiv:1401.2975 [INSPIRE]."},{"key":"8968_CR6","unstructured":"S. Giombi, Higher Spin \u2014 CFT Duality, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015), Boulder, CO, U.S.A., June 1-26, 2015, pp. 137-214 (2017) [DOI:10.1142\/9789813149441 0003] [arXiv:1607.02967] [INSPIRE]."},{"key":"8968_CR7","doi-asserted-by":"crossref","unstructured":"E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th\/9802150] [INSPIRE].","DOI":"10.4310\/ATMP.1998.v2.n2.a2"},{"key":"8968_CR8","doi-asserted-by":"crossref","unstructured":"W. Mueck and K.S. Viswanathan, Conformal field theory correlators from classical scalar field theory on AdS(d+1), Phys. Rev. D 58 (1998) 041901 [hep-th\/9804035] [INSPIRE].","DOI":"10.1103\/PhysRevD.58.041901"},{"key":"8968_CR9","doi-asserted-by":"crossref","unstructured":"D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT(d)\/AdS(d+1) correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th\/9804058] [INSPIRE].","DOI":"10.1016\/S0550-3213(99)00053-X"},{"key":"8968_CR10","doi-asserted-by":"crossref","unstructured":"H. Liu and A.A. Tseytlin, On four point functions in the CFT\/AdS correspondence, Phys. Rev. D 59 (1999) 086002 [hep-th\/9807097] [INSPIRE].","DOI":"10.1103\/PhysRevD.59.086002"},{"key":"8968_CR11","doi-asserted-by":"crossref","unstructured":"D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Comments on 4 point functions in the CFT\/AdS correspondence, Phys. Lett. B 452 (1999) 61 [hep-th\/9808006] [INSPIRE].","DOI":"10.1016\/S0370-2693(99)00229-4"},{"key":"8968_CR12","doi-asserted-by":"crossref","unstructured":"H. Liu, Scattering in anti-de Sitter space and operator product expansion, Phys. Rev. D 60 (1999) 106005 [hep-th\/9811152] [INSPIRE].","DOI":"10.1103\/PhysRevD.60.106005"},{"key":"8968_CR13","doi-asserted-by":"crossref","unstructured":"E. D\u2019Hoker and D.Z. Freedman, General scalar exchange in AdS(d+1), Nucl. Phys. B 550 (1999) 261 [hep-th\/9811257] [INSPIRE].","DOI":"10.1016\/S0550-3213(99)00169-8"},{"key":"8968_CR14","doi-asserted-by":"crossref","unstructured":"E. D\u2019Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton exchange and complete four point functions in the AdS\/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th\/9903196] [INSPIRE].","DOI":"10.1016\/S0550-3213(99)00525-8"},{"key":"8968_CR15","doi-asserted-by":"crossref","unstructured":"E. D\u2019Hoker, S.D. Mathur, A. Matusis and L. Rastelli, The Operator product expansion of N = 4 SYM and the 4 point functions of supergravity, Nucl. Phys. B 589 (2000) 38 [hep-th\/9911222] [INSPIRE].","DOI":"10.1016\/S0550-3213(00)00523-X"},{"key":"8968_CR16","doi-asserted-by":"crossref","unstructured":"E. D\u2019Hoker, D.Z. Freedman and L. Rastelli, AdS\/CFT four point functions: How to succeed at z integrals without really trying, Nucl. Phys. B 562 (1999) 395 [hep-th\/9905049] [INSPIRE].","DOI":"10.1016\/S0550-3213(99)00526-X"},{"key":"8968_CR17","doi-asserted-by":"crossref","unstructured":"L. Hoffmann, A.C. Petkou and W. R\u00fchl, Aspects of the conformal operator product expansion in AdS\/CFT correspondence, Adv. Theor. Math. Phys. 4 (2002) 571 [hep-th\/0002154] [INSPIRE].","DOI":"10.4310\/ATMP.2000.v4.n3.a3"},{"key":"8968_CR18","doi-asserted-by":"crossref","unstructured":"G. Arutyunov, F.A. Dolan, H. Osborn and E. Sokatchev, Correlation functions and massive Kaluza-Klein modes in the AdS\/CFT correspondence, Nucl. Phys. B 665 (2003) 273 [hep-th\/0212116] [INSPIRE].","DOI":"10.1016\/S0550-3213(03)00448-6"},{"key":"8968_CR19","doi-asserted-by":"crossref","unstructured":"M.S. Costa, V. Gon\u00e7alves and J. Penedones, Spinning AdS Propagators, JHEP 09 (2014) 064 [arXiv:1404.5625] [INSPIRE].","DOI":"10.1007\/JHEP09(2014)064"},{"key":"8968_CR20","doi-asserted-by":"crossref","unstructured":"X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange, JHEP 03 (2015) 170 [arXiv:1412.0016] [INSPIRE].","DOI":"10.1007\/JHEP03(2015)170"},{"key":"8968_CR21","doi-asserted-by":"crossref","unstructured":"E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks, JHEP 01 (2016) 146 [arXiv:1508.00501] [INSPIRE].","DOI":"10.1007\/JHEP01(2016)146"},{"key":"8968_CR22","doi-asserted-by":"crossref","unstructured":"C. Sleight and M. Taronna, Spinning Witten Diagrams, JHEP 06 (2017) 100 [arXiv:1702.08619] [INSPIRE].","DOI":"10.1007\/JHEP06(2017)100"},{"key":"8968_CR23","doi-asserted-by":"crossref","unstructured":"M. Nishida and K. Tamaoka, Geodesic Witten diagrams with an external spinning field, PTEP 2017 (2017) 053B06 [arXiv:1609.04563] [INSPIRE].","DOI":"10.1093\/ptep\/ptx055"},{"key":"8968_CR24","doi-asserted-by":"crossref","unstructured":"A. Castro, E. Llabr\u00e9s and F. Rejon-Barrera, Geodesic Diagrams, Gravitational Interactions & OPE Structures, JHEP 06 (2017) 099 [arXiv:1702.06128] [INSPIRE].","DOI":"10.1007\/JHEP06(2017)099"},{"key":"8968_CR25","doi-asserted-by":"publisher","first-page":"060","DOI":"10.1007\/JHEP11(2017)060","volume":"11","author":"E Dyer","year":"2017","unstructured":"E. Dyer, D.Z. Freedman and J. Sully, Spinning Geodesic Witten Diagrams, JHEP 11 (2017) 060 [arXiv:1702.06139] [INSPIRE].","journal-title":"JHEP"},{"key":"8968_CR26","doi-asserted-by":"publisher","first-page":"070","DOI":"10.1007\/JHEP05(2017)070","volume":"05","author":"H-Y Chen","year":"2017","unstructured":"H.-Y. Chen, E.-J. Kuo and H. Kyono, Anatomy of Geodesic Witten Diagrams, JHEP 05 (2017) 070 [arXiv:1702.08818] [INSPIRE].","journal-title":"JHEP"},{"key":"8968_CR27","doi-asserted-by":"crossref","unstructured":"L. Cornalba, M.S. Costa and J. Penedones, Eikonal approximation in AdS\/CFT: Resumming the gravitational loop expansion, JHEP 09 (2007) 037 [arXiv:0707.0120] [INSPIRE].","DOI":"10.1088\/1126-6708\/2007\/09\/037"},{"key":"8968_CR28","doi-asserted-by":"crossref","unstructured":"J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].","DOI":"10.1007\/JHEP03(2011)025"},{"key":"8968_CR29","doi-asserted-by":"crossref","unstructured":"A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].","DOI":"10.1007\/JHEP10(2012)127"},{"key":"8968_CR30","doi-asserted-by":"crossref","unstructured":"A.L. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].","DOI":"10.1007\/JHEP10(2012)032"},{"key":"8968_CR31","doi-asserted-by":"crossref","unstructured":"O. Aharony, L.F. Alday, A. Bissi and E. Perlmutter, Loops in AdS from Conformal Field Theory, JHEP 07 (2017) 036 [arXiv:1612.03891] [INSPIRE].","DOI":"10.1007\/JHEP07(2017)036"},{"key":"8968_CR32","doi-asserted-by":"crossref","unstructured":"L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS 5 \u00d7 S 5, Phys. Rev. Lett. 119 (2017) 171601 [arXiv:1706.02388] [INSPIRE].","DOI":"10.1103\/PhysRevLett.119.171601"},{"key":"8968_CR33","unstructured":"C. Cardona, Mellin-(Schwinger) representation of One-loop Witten diagrams in AdS, arXiv:1708.06339 [INSPIRE]."},{"key":"8968_CR34","doi-asserted-by":"crossref","unstructured":"S. Giombi, C. Sleight and M. Taronna, Spinning AdS Loop Diagrams: Two Point Functions, JHEP 06 (2018) 030 [arXiv:1708.08404] [INSPIRE].","DOI":"10.1007\/JHEP06(2018)030"},{"key":"8968_CR35","unstructured":"I. Bertan and I. Sachs, Loops in Anti-de Sitter Space, arXiv:1804.01880 [INSPIRE]."},{"key":"8968_CR36","doi-asserted-by":"crossref","unstructured":"P. Mansfield and D. Nolland, Order 1\/N**2 test of the Maldacena conjecture: Cancellation of the one loop Weyl anomaly, Phys. Lett. B 495 (2000) 435 [hep-th\/0005224] [INSPIRE].","DOI":"10.1016\/S0370-2693(00)01247-8"},{"key":"8968_CR37","doi-asserted-by":"publisher","first-page":"007","DOI":"10.1088\/1126-6708\/2008\/08\/007","volume":"08","author":"S Giombi","year":"2008","unstructured":"S. Giombi, A. Maloney and X. Yin, One-loop Partition Functions of 3D Gravity, JHEP 08 (2008) 007 [arXiv:0804.1773] [INSPIRE].","journal-title":"JHEP"},{"key":"8968_CR38","doi-asserted-by":"crossref","unstructured":"R. Gopakumar, R.K. Gupta and S. Lal, The Heat Kernel on AdS, JHEP 11 (2011) 010 [arXiv:1103.3627] [INSPIRE].","DOI":"10.1007\/JHEP11(2011)010"},{"key":"8968_CR39","doi-asserted-by":"publisher","first-page":"068","DOI":"10.1007\/JHEP12(2013)068","volume":"12","author":"S Giombi","year":"2013","unstructured":"S. Giombi and I.R. Klebanov, One Loop Tests of Higher Spin AdS\/CFT, JHEP 12 (2013) 068 [arXiv:1308.2337] [INSPIRE].","journal-title":"JHEP"},{"key":"8968_CR40","doi-asserted-by":"crossref","unstructured":"A. Arabi Ardehali, J.T. Liu and P. Szepietowski, 1\/N 2 corrections to the holographic Weyl anomaly, JHEP 01 (2014) 002 [arXiv:1310.2611] [INSPIRE].","DOI":"10.1007\/JHEP01(2014)002"},{"key":"8968_CR41","doi-asserted-by":"crossref","unstructured":"M. Beccaria and A.A. Tseytlin, Higher spins in AdS 5 at one loop: vacuum energy, boundary conformal anomalies and AdS\/CFT, JHEP 11 (2014) 114 [arXiv:1410.3273] [INSPIRE].","DOI":"10.1007\/JHEP11(2014)114"},{"key":"8968_CR42","first-page":"061","volume":"04","author":"J-B Bae","year":"2016","unstructured":"J.-B. Bae, E. Joung and S. Lal, One-loop test of free SU(N) adjoint model holography, JHEP 04 (2016) 061 [arXiv:1603.05387] [INSPIRE].","journal-title":"JHEP"},{"key":"8968_CR43","doi-asserted-by":"crossref","unstructured":"J.-B. Bae, E. Joung and S. Lal, On the Holography of Free Yang-Mills, JHEP 10 (2016) 074 [arXiv:1607.07651] [INSPIRE].","DOI":"10.1007\/JHEP10(2016)074"},{"key":"8968_CR44","doi-asserted-by":"crossref","unstructured":"J.-B. Bae, E. Joung and S. Lal, One-loop free energy of tensionless type IIB string in AdS 5 \u00d7 S 5, JHEP 06 (2017) 155 [arXiv:1701.01507] [INSPIRE].","DOI":"10.1007\/JHEP06(2017)155"},{"key":"8968_CR45","doi-asserted-by":"crossref","unstructured":"E.D. Skvortsov and T. Tran, AdS\/CFT in Fractional Dimension and Higher Spin Gravity at One Loop, Universe 3 (2017) 61 [arXiv:1707.00758] [INSPIRE].","DOI":"10.3390\/universe3030061"},{"key":"8968_CR46","doi-asserted-by":"crossref","unstructured":"D. Karateev, P. Kravchuk and D. Simmons-Duffin, Weight Shifting Operators and Conformal Blocks, JHEP 02 (2018) 081 [arXiv:1706.07813] [INSPIRE].","DOI":"10.1007\/JHEP02(2018)081"},{"key":"8968_CR47","doi-asserted-by":"crossref","unstructured":"X. Bekaert and E. Meunier, Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions, JHEP 11 (2010) 116 [arXiv:1007.4384] [INSPIRE].","DOI":"10.1007\/JHEP11(2010)116"},{"key":"8968_CR48","doi-asserted-by":"crossref","unstructured":"C. Sleight, Metric-like Methods in Higher Spin Holography, PoS(Modave2016)003 [arXiv:1701.08360] [INSPIRE].","DOI":"10.22323\/1.296.0003"},{"key":"8968_CR49","doi-asserted-by":"crossref","unstructured":"M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].","DOI":"10.1007\/JHEP11(2011)071"},{"key":"8968_CR50","unstructured":"L. Cornalba, Eikonal methods in AdS\/CFT: Regge theory and multi-reggeon exchange, arXiv:0710.5480 [INSPIRE]."},{"key":"8968_CR51","doi-asserted-by":"crossref","unstructured":"X. Bekaert and M. Grigoriev, Notes on the ambient approach to boundary values of AdS gauge fields, J. Phys. A 46 (2013) 214008 [arXiv:1207.3439] [INSPIRE].","DOI":"10.1088\/1751-8113\/46\/21\/214008"},{"key":"8968_CR52","doi-asserted-by":"crossref","unstructured":"M.S. Costa and T. Hansen, Conformal correlators of mixed-symmetry tensors, JHEP 02 (2015) 151 [arXiv:1411.7351] [INSPIRE].","DOI":"10.1007\/JHEP02(2015)151"},{"key":"8968_CR53","doi-asserted-by":"crossref","unstructured":"M.S. Costa, T. Hansen, J. Penedones and E. Trevisani, Projectors and seed conformal blocks for traceless mixed-symmetry tensors, JHEP 07 (2016) 018 [arXiv:1603.05551] [INSPIRE].","DOI":"10.1007\/JHEP07(2016)018"},{"key":"8968_CR54","doi-asserted-by":"crossref","unstructured":"P. Kravchuk and D. Simmons-Duffin, Counting Conformal Correlators, JHEP 02 (2018) 096 [arXiv:1612.08987] [INSPIRE].","DOI":"10.1007\/JHEP02(2018)096"},{"key":"8968_CR55","doi-asserted-by":"crossref","unstructured":"F.A. Berends, G.J.H. Burgers and H. van Dam, Explicit Construction of Conserved Currents for Massless Fields of Arbitrary Spin, Nucl. Phys. B 271 (1986) 429 [INSPIRE].","DOI":"10.1016\/0550-3213(86)90325-1"},{"key":"8968_CR56","doi-asserted-by":"crossref","unstructured":"R.R. Metsaev, Cubic interaction vertices of massive and massless higher spin fields, Nucl. Phys. B 759 (2006) 147 [hep-th\/0512342] [INSPIRE].","DOI":"10.1016\/j.nuclphysb.2006.10.002"},{"key":"8968_CR57","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1007\/JHEP11(2011)154","volume":"11","author":"MS Costa","year":"2011","unstructured":"M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Blocks, JHEP 11 (2011) 154 [arXiv:1109.6321] [INSPIRE].","journal-title":"JHEP"},{"key":"8968_CR58","doi-asserted-by":"crossref","unstructured":"P. Cvitanovic, Group theory: Birdtracks, Lie\u2019s and exceptional groups, Princeton University Press (2008).","DOI":"10.1515\/9781400837670"},{"key":"8968_CR59","doi-asserted-by":"crossref","unstructured":"K. Krasnov and J. Louko, SO(1, d + 1) Racah coefficients: Type I representations, J. Math. Phys. 47 (2006) 033513 [math-ph\/0502017] [INSPIRE].","DOI":"10.1063\/1.2180626"},{"key":"8968_CR60","doi-asserted-by":"crossref","unstructured":"M. Nishida and K. Tamaoka, Fermions in Geodesic Witten Diagrams, JHEP 07 (2018) 149 [arXiv:1805.00217] [INSPIRE].","DOI":"10.1007\/JHEP07(2018)149"},{"key":"8968_CR61","doi-asserted-by":"publisher","first-page":"060","DOI":"10.1007\/JHEP01(2018)060","volume":"01","author":"C Sleight","year":"2018","unstructured":"C. Sleight and M. Taronna, Feynman rules for higher-spin gauge fields on AdS d+1, JHEP 01 (2018) 060 [arXiv:1708.08668] [INSPIRE].","journal-title":"JHEP"},{"key":"8968_CR62","unstructured":"R. Rahman and M. Taronna, From Higher Spins to Strings: A Primer, arXiv:1512.07932 [INSPIRE]."}],"container-title":["Journal of High Energy Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP09(2018)040.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/JHEP09(2018)040\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP09(2018)040.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T00:47:46Z","timestamp":1751849266000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/JHEP09(2018)040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9]]},"references-count":62,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["8968"],"URL":"https:\/\/doi.org\/10.1007\/jhep09(2018)040","relation":{},"ISSN":["1029-8479"],"issn-type":[{"value":"1029-8479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9]]},"assertion":[{"value":"29 June 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"40"}}