(2,0) Theory on × and quantum M2 branes

M. Beccaria (Università del Salento, Dipartimento di Matematica e Fisica Ennio De Giorgi, I.N.F.N., sezione di Lecce, Via Arnesano, Lecce, Italy) ; S. Giombi (Department of Physics, Princeton University, Princeton, USA) ; A.A. Tseytlin (Blackett Laboratory, Imperial College, London, UK)

The superconformal index Z of the 6d (2,0) theory on S5×S1 (which is related to the localization partition function of 5d SYM on S5) 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 S4. 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 S1×S2 with S2S4. 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 AdS3 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×4S7/Zk which reproduced the corresponding localization expressions in the ABJM 3d gauge theory.

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      "surname": "Giombi", 
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      "title": "(2,0) Theory on \u00d7 and quantum M2 branes"
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      "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."
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Published on:
17 November 2023
Publisher:
Elsevier
Published in:
Nuclear Physics B , Volume 998 C (2023)

Article ID: 116400
DOI:
https://doi.org/10.1016/j.nuclphysb.2023.116400
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: