An N=1 3d-3d correspondence
M5-branes on an associative three-cycle M3 in a G2-holonomy manifold give rise to a 3d N = 1 supersymmetric gauge theory, TN=1[M3]. We propose an N = 1 3d-3d correspondence, based on two observables of these theories: the Witten index and the S3-partition function. The Witten index of a 3d N = 1 the...
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| 格式: | Journal article |
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Springer
2018
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| _version_ | 1826305931209605120 |
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| author | Eckhard, J Schafer-Nameki, S Wong, J-M |
| author_facet | Eckhard, J Schafer-Nameki, S Wong, J-M |
| author_sort | Eckhard, J |
| collection | OXFORD |
| description | M5-branes on an associative three-cycle M3 in a G2-holonomy manifold give rise to a 3d N = 1 supersymmetric gauge theory, TN=1[M3]. We propose an N = 1 3d-3d correspondence, based on two observables of these theories: the Witten index and the S3-partition function. The Witten index of a 3d N = 1 theory TN=1[M3] is shown to be computed in terms of the partition function of a topological field theory, a super-BF-model coupled to a spinorial hypermultiplet (BFH), on M3. The BFH-model localizes on solutions to a generalized set of 3d Seiberg-Witten equations on M3. Evidence to support this correspondence is provided in the abelian case, as well as in terms of a direct derivation of the topological field theory by twisted dimensional reduction of the 6d (2; 0) theory. We also consider a correspondence for the S3-partition function of the TN=1[M3] theories, by determining the dimensional reduction of the M5-brane theory on S3. The resulting topological theory is Chern-Simons-Dirac theory, for a gauge field and a twisted harmonic spinor on M3, whose equations of motion are the generalized 3d Seiberg-Witten equations. For generic G2-manifolds the theory reduces to real Chern-Simons theory, in which case we conjecture that the S3-partition function of TN=1[M3] is given by the Witten-Reshetikhin-Turaev invariant of M3. |
| first_indexed | 2024-03-07T06:40:17Z |
| format | Journal article |
| id | oxford-uuid:f90c79db-6c4d-427a-83c6-cab90b2c4848 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:40:17Z |
| publishDate | 2018 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:f90c79db-6c4d-427a-83c6-cab90b2c48482022-03-27T12:55:00ZAn N=1 3d-3d correspondenceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f90c79db-6c4d-427a-83c6-cab90b2c4848Symplectic Elements at OxfordSpringer2018Eckhard, JSchafer-Nameki, SWong, J-MM5-branes on an associative three-cycle M3 in a G2-holonomy manifold give rise to a 3d N = 1 supersymmetric gauge theory, TN=1[M3]. We propose an N = 1 3d-3d correspondence, based on two observables of these theories: the Witten index and the S3-partition function. The Witten index of a 3d N = 1 theory TN=1[M3] is shown to be computed in terms of the partition function of a topological field theory, a super-BF-model coupled to a spinorial hypermultiplet (BFH), on M3. The BFH-model localizes on solutions to a generalized set of 3d Seiberg-Witten equations on M3. Evidence to support this correspondence is provided in the abelian case, as well as in terms of a direct derivation of the topological field theory by twisted dimensional reduction of the 6d (2; 0) theory. We also consider a correspondence for the S3-partition function of the TN=1[M3] theories, by determining the dimensional reduction of the M5-brane theory on S3. The resulting topological theory is Chern-Simons-Dirac theory, for a gauge field and a twisted harmonic spinor on M3, whose equations of motion are the generalized 3d Seiberg-Witten equations. For generic G2-manifolds the theory reduces to real Chern-Simons theory, in which case we conjecture that the S3-partition function of TN=1[M3] is given by the Witten-Reshetikhin-Turaev invariant of M3. |
| spellingShingle | Eckhard, J Schafer-Nameki, S Wong, J-M An N=1 3d-3d correspondence |
| title | An N=1 3d-3d correspondence |
| title_full | An N=1 3d-3d correspondence |
| title_fullStr | An N=1 3d-3d correspondence |
| title_full_unstemmed | An N=1 3d-3d correspondence |
| title_short | An N=1 3d-3d correspondence |
| title_sort | n 1 3d 3d correspondence |
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