The superconformal index Z of the 6d (2,0) theory on (which is related to the localization partition function of 5d SYM on ) should be captured at large N by the quantum M2 brane theory in the dual M-theory background. Generalizing the type IIA string theory limit of this relation discussed in arXiv:2111.15493 and arXiv:2304.12340, we consider semiclassically quantized M2 branes in a half-supersymmetric 11d background which is a twisted product of thermal AdS$_{7}$ and . We show that the leading non-perturbative term at large N is reproduced precisely by the 1-loop partition function of an “instanton” M2 brane wrapped on with . Similarly, the (2,0) theory analog of the BPS Wilson loop expectation value is reproduced by the partition function of a “defect” M2 brane wrapped on thermal AdS AdS$_{7}$. We comment on a curious analogy of these results with similar computations in arXiv:2303.15207 and arXiv:2307.14112 of the partition function of quantum M2 branes in AdS which reproduced the corresponding localization expressions in the ABJM 3d gauge theory.
{ "license": [ { "url": "http://creativecommons.org/licenses/by/3.0/", "license": "CC-BY-3.0" } ], "copyright": [ { "holder": "The Author(s)", "statement": "The Author(s)", "year": "2023" } ], "control_number": "81503", "_oai": { "updated": "2025-01-11T09:30:33Z", "id": "oai:repo.scoap3.org:81503", "sets": [ "NPB" ] }, "authors": [ { "affiliations": [ { "country": "Italy", "value": "Universit\u00e0 del Salento, Dipartimento di Matematica e Fisica Ennio De Giorgi, I.N.F.N., sezione di Lecce, Via Arnesano, Lecce, Italy" } ], "surname": "Beccaria", "email": "matteo.beccaria@le.infn.it", "full_name": "Beccaria, M.", "given_names": "M." }, { "affiliations": [ { "country": "USA", "value": "Department of Physics, Princeton University, Princeton, USA" } ], "surname": "Giombi", "email": "sgiombi@princeton.edu", "full_name": "Giombi, S.", "given_names": "S." }, { "surname": "Tseytlin", "given_names": "A.A.", "affiliations": [ { "country": "UK", "value": "Blackett Laboratory, Imperial College, London, UK" } ], "full_name": "Tseytlin, A.A.", "orcid": "0000-0002-5066-8282", "email": "tseytlin@imperial.ac.uk" } ], "_files": [ { "checksum": "md5:5e226321e6e923da0eb9fb6866db05a0", "filetype": "xml", "bucket": "8d9e7bed-18dc-409d-80fc-cbb382997572", "version_id": "04211749-c6cd-43f1-b66b-84e228674a2d", "key": "10.1016/j.nuclphysb.2023.116400.xml", "size": 727030 }, { "checksum": "md5:b372f6248e854e8c8108ee8a66615684", "filetype": "pdf", "bucket": "8d9e7bed-18dc-409d-80fc-cbb382997572", "version_id": "93b535bb-378a-4966-bf7d-eb70e425de1e", "key": "10.1016/j.nuclphysb.2023.116400.pdf", "size": 843499 } ], "record_creation_date": "2023-11-21T21:30:25.825585", "titles": [ { "source": "Elsevier", "title": "(2,0) Theory on \u00d7 and quantum M2 branes" } ], "collections": [ { "primary": "Nuclear Physics B" } ], "dois": [ { "value": "10.1016/j.nuclphysb.2023.116400" } ], "publication_info": [ { "journal_volume": "998 C", "journal_title": "Nuclear Physics B", "material": "article", "artid": "116400", "year": 2023 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "abstracts": [ { "source": "Elsevier", "value": "The superconformal index Z of the 6d (2,0) theory on <math><msup><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msup><mo>\u00d7</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math> (which is related to the localization partition function of 5d SYM on <math><msup><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msup></math>) should be captured at large N by the quantum M2 brane theory in the dual M-theory background. Generalizing the type IIA string theory limit of this relation discussed in arXiv:2111.15493 and arXiv:2304.12340, we consider semiclassically quantized M2 branes in a half-supersymmetric 11d background which is a twisted product of thermal AdS$_{7}$ and <math><msup><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msup></math>. We show that the leading non-perturbative term at large N is reproduced precisely by the 1-loop partition function of an \u201cinstanton\u201d M2 brane wrapped on <math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>\u00d7</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math> with <math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>\u2282</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msup></math>. Similarly, the (2,0) theory analog of the BPS Wilson loop expectation value is reproduced by the partition function of a \u201cdefect\u201d M2 brane wrapped on thermal AdS<math><mmultiscripts><mrow><mo>\u2282</mo></mrow><mprescripts></mprescripts><mrow><mn>3</mn></mrow><none></none></mmultiscripts></math> AdS$_{7}$. We comment on a curious analogy of these results with similar computations in arXiv:2303.15207 and arXiv:2307.14112 of the partition function of quantum M2 branes in AdS<math><mmultiscripts><mrow><mo>\u00d7</mo></mrow><mprescripts></mprescripts><mrow><mn>4</mn></mrow><none></none></mmultiscripts><msup><mrow><mi>S</mi></mrow><mrow><mn>7</mn></mrow></msup><mo>/</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub></math> which reproduced the corresponding localization expressions in the ABJM 3d gauge theory." } ], "imprints": [ { "date": "2023-11-17", "publisher": "Elsevier" } ], "acquisition_source": { "date": "2025-01-11T09:30:30.052279", "source": "Elsevier", "method": "Elsevier", "submission_number": "a0ec0382cffe11ef8ffe02401effc807" } }