Partition functions and fibering operators on the Coulomb branch of 5d SCFTs
Abstract We study 5d N $$ \mathcal{N} $$ = 1 supersymmetric field theories on closed five-manifolds M $$ \mathcal{M} $$ 5 which are principal circle bundles over simply-connected Kähler four-manifolds, M $$ \mathcal{M} $$ 4, equipped with the Donaldson-Witten twist. We propose a new approach to comp...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2023)035 |
| _version_ | 1797836703870746624 |
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| author | Cyril Closset Horia Magureanu |
| author_facet | Cyril Closset Horia Magureanu |
| author_sort | Cyril Closset |
| collection | DOAJ |
| description | Abstract We study 5d N $$ \mathcal{N} $$ = 1 supersymmetric field theories on closed five-manifolds M $$ \mathcal{M} $$ 5 which are principal circle bundles over simply-connected Kähler four-manifolds, M $$ \mathcal{M} $$ 4, equipped with the Donaldson-Witten twist. We propose a new approach to compute the supersymmetric partition function on M $$ \mathcal{M} $$ 5 through the insertion of a fibering operator, which introduces a non-trivial fibration over M $$ \mathcal{M} $$ 4, in the 4d topologically twisted field theory. We determine the so-called Coulomb branch partition function on any such M $$ \mathcal{M} $$ 5, which is conjectured to be the holomorphic ‘integrand’ of the full partition function. We precisely match the low-energy effective field theory approach to explicit one-loop computations, and we discuss the effect of non-perturbative 5d BPS particles in this context. When M $$ \mathcal{M} $$ 4 is toric, we also reconstruct our Coulomb branch partition function by appropriately gluing Nekrasov partition functions. As a by-product of our analysis, we provide strong new evidence for the validity of the Lockhart-Vafa formula for the five-sphere partition function. |
| first_indexed | 2024-04-09T15:13:14Z |
| format | Article |
| id | doaj.art-b82471e2298840088af41a14ad880678 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T15:13:14Z |
| publishDate | 2023-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-b82471e2298840088af41a14ad8806782023-04-30T11:03:57ZengSpringerOpenJournal of High Energy Physics1029-84792023-01-012023118810.1007/JHEP01(2023)035Partition functions and fibering operators on the Coulomb branch of 5d SCFTsCyril Closset0Horia Magureanu1School of Mathematics, University of BirminghamMathematical Institute, University of OxfordAbstract We study 5d N $$ \mathcal{N} $$ = 1 supersymmetric field theories on closed five-manifolds M $$ \mathcal{M} $$ 5 which are principal circle bundles over simply-connected Kähler four-manifolds, M $$ \mathcal{M} $$ 4, equipped with the Donaldson-Witten twist. We propose a new approach to compute the supersymmetric partition function on M $$ \mathcal{M} $$ 5 through the insertion of a fibering operator, which introduces a non-trivial fibration over M $$ \mathcal{M} $$ 4, in the 4d topologically twisted field theory. We determine the so-called Coulomb branch partition function on any such M $$ \mathcal{M} $$ 5, which is conjectured to be the holomorphic ‘integrand’ of the full partition function. We precisely match the low-energy effective field theory approach to explicit one-loop computations, and we discuss the effect of non-perturbative 5d BPS particles in this context. When M $$ \mathcal{M} $$ 4 is toric, we also reconstruct our Coulomb branch partition function by appropriately gluing Nekrasov partition functions. As a by-product of our analysis, we provide strong new evidence for the validity of the Lockhart-Vafa formula for the five-sphere partition function.https://doi.org/10.1007/JHEP01(2023)035Nonperturbative EffectsSupersymmetric Effective TheoriesSupersymmetric Gauge Theory |
| spellingShingle | Cyril Closset Horia Magureanu Partition functions and fibering operators on the Coulomb branch of 5d SCFTs Journal of High Energy Physics Nonperturbative Effects Supersymmetric Effective Theories Supersymmetric Gauge Theory |
| title | Partition functions and fibering operators on the Coulomb branch of 5d SCFTs |
| title_full | Partition functions and fibering operators on the Coulomb branch of 5d SCFTs |
| title_fullStr | Partition functions and fibering operators on the Coulomb branch of 5d SCFTs |
| title_full_unstemmed | Partition functions and fibering operators on the Coulomb branch of 5d SCFTs |
| title_short | Partition functions and fibering operators on the Coulomb branch of 5d SCFTs |
| title_sort | partition functions and fibering operators on the coulomb branch of 5d scfts |
| topic | Nonperturbative Effects Supersymmetric Effective Theories Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP01(2023)035 |
| work_keys_str_mv | AT cyrilclosset partitionfunctionsandfiberingoperatorsonthecoulombbranchof5dscfts AT horiamagureanu partitionfunctionsandfiberingoperatorsonthecoulombbranchof5dscfts |