Coulomb branch operator algebras and universal selection rules for N $$ \mathcal{N} $$ = 2 SCFTs
Abstract Coulomb branches of vacua are the most universal moduli spaces that arise in local unitary interacting 4d N $$ \mathcal{N} $$ = 2 superconformal field theories (SCFTs). In these theories, 1/2-BPS primaries parameterize the Coulomb branches and form (anti-)chiral rings. We define the notion...
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2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)212 |
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| author | Matthew Buican |
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| author_sort | Matthew Buican |
| collection | DOAJ |
| description | Abstract Coulomb branches of vacua are the most universal moduli spaces that arise in local unitary interacting 4d N $$ \mathcal{N} $$ = 2 superconformal field theories (SCFTs). In these theories, 1/2-BPS primaries parameterize the Coulomb branches and form (anti-)chiral rings. We define the notion of a Coulomb branch operator algebra, A C $$ {\mathcal{A}}_{\mathcal{C}} $$ , that contains these chiral and anti-chiral rings along with infinitely many more operators and products that are less protected by supersymmetry. Using a universal symmetry, I ≅ ℤ 2 $$ \mathcal{I}\cong {\mathbb{Z}}_2 $$ , that arises from studying the superconformal group, we give I $$ \mathcal{I} $$ selection rules for A C $$ {\mathcal{A}}_{\mathcal{C}} $$ and, more generally, for arbitrary products in the local operator algebra of any 4d N $$ \mathcal{N} $$ = 2 SCFT. Defining the notion of a “Coulombic” SCFT, we propose explanations for certain phenomena in a 4d/2d correspondence involving 4d N $$ \mathcal{N} $$ = 2 theories and 2d vertex operator algebras. Finally, by considering deformations of I $$ \mathcal{I} $$ , we explore the case of N $$ \mathcal{N} $$ > 2 SCFTs. |
| format | Article |
| id | doaj-art-a9ee80bb88b14280aee6a9a142f13256 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-a9ee80bb88b14280aee6a9a142f132562025-08-20T03:42:34ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025712410.1007/JHEP07(2025)212Coulomb branch operator algebras and universal selection rules for N $$ \mathcal{N} $$ = 2 SCFTsMatthew Buican0CTP and Department of Physics and Astronomy, Queen Mary University of LondonAbstract Coulomb branches of vacua are the most universal moduli spaces that arise in local unitary interacting 4d N $$ \mathcal{N} $$ = 2 superconformal field theories (SCFTs). In these theories, 1/2-BPS primaries parameterize the Coulomb branches and form (anti-)chiral rings. We define the notion of a Coulomb branch operator algebra, A C $$ {\mathcal{A}}_{\mathcal{C}} $$ , that contains these chiral and anti-chiral rings along with infinitely many more operators and products that are less protected by supersymmetry. Using a universal symmetry, I ≅ ℤ 2 $$ \mathcal{I}\cong {\mathbb{Z}}_2 $$ , that arises from studying the superconformal group, we give I $$ \mathcal{I} $$ selection rules for A C $$ {\mathcal{A}}_{\mathcal{C}} $$ and, more generally, for arbitrary products in the local operator algebra of any 4d N $$ \mathcal{N} $$ = 2 SCFT. Defining the notion of a “Coulombic” SCFT, we propose explanations for certain phenomena in a 4d/2d correspondence involving 4d N $$ \mathcal{N} $$ = 2 theories and 2d vertex operator algebras. Finally, by considering deformations of I $$ \mathcal{I} $$ , we explore the case of N $$ \mathcal{N} $$ > 2 SCFTs.https://doi.org/10.1007/JHEP07(2025)212Extended SupersymmetryNonperturbative EffectsScale and Conformal SymmetriesSupersymmetric Gauge Theory |
| spellingShingle | Matthew Buican Coulomb branch operator algebras and universal selection rules for N $$ \mathcal{N} $$ = 2 SCFTs Journal of High Energy Physics Extended Supersymmetry Nonperturbative Effects Scale and Conformal Symmetries Supersymmetric Gauge Theory |
| title | Coulomb branch operator algebras and universal selection rules for N $$ \mathcal{N} $$ = 2 SCFTs |
| title_full | Coulomb branch operator algebras and universal selection rules for N $$ \mathcal{N} $$ = 2 SCFTs |
| title_fullStr | Coulomb branch operator algebras and universal selection rules for N $$ \mathcal{N} $$ = 2 SCFTs |
| title_full_unstemmed | Coulomb branch operator algebras and universal selection rules for N $$ \mathcal{N} $$ = 2 SCFTs |
| title_short | Coulomb branch operator algebras and universal selection rules for N $$ \mathcal{N} $$ = 2 SCFTs |
| title_sort | coulomb branch operator algebras and universal selection rules for n mathcal n 2 scfts |
| topic | Extended Supersymmetry Nonperturbative Effects Scale and Conformal Symmetries Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP07(2025)212 |
| work_keys_str_mv | AT matthewbuican coulombbranchoperatoralgebrasanduniversalselectionrulesfornmathcaln2scfts |