Minimally extended current algebras of toroidal conformal field theories
Abstract It is well-known that families of two-dimensional toroidal conformal field theories possess a dense subset of rational toroidal conformal field theories, which makes such families an interesting testing ground about rationality of conformal field theories in families in general. Rational to...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-07-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2024)187 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850204473657393152 |
|---|---|
| author | Hans Jockers Maik Sarve Ida G. Zadeh |
| author_facet | Hans Jockers Maik Sarve Ida G. Zadeh |
| author_sort | Hans Jockers |
| collection | DOAJ |
| description | Abstract It is well-known that families of two-dimensional toroidal conformal field theories possess a dense subset of rational toroidal conformal field theories, which makes such families an interesting testing ground about rationality of conformal field theories in families in general. Rational toroidal conformal field theories possess an extended chiral and anti-chiral algebra known as W-algebras. Their partition functions decompose into a finite sum of products of holomorphic and anti-holomorphic characters of these W-algebras. Instead of considering these characters, we decompose the partition functions into products of characters of minimal extensions of u ̂ 1 $$ \hat{\mathfrak{u}}(1) $$ current algebras, which already appear for rational conformal field theories with target space S 1. We present an explicit construction that determines such decompositions. While these decompositions are not unique, they are universal in the sense that any rational toroidal conformal field theory with a target space torus of arbitrary dimension admits such decompositions. We illustrate these decompositions with a few representative examples of rational toroidal conformal field theories with two- and three-dimensional target space tori. |
| format | Article |
| id | doaj-art-e1c2a1ab44fa494c9e37e57767801ed2 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-e1c2a1ab44fa494c9e37e57767801ed22025-08-20T02:11:17ZengSpringerOpenJournal of High Energy Physics1029-84792024-07-012024712110.1007/JHEP07(2024)187Minimally extended current algebras of toroidal conformal field theoriesHans Jockers0Maik Sarve1Ida G. Zadeh2PRISMA+ Cluster of Excellence & Mainz Institute for Theoretical Physics, Johannes Guttenberg-UniversitätPRISMA+ Cluster of Excellence & Mainz Institute for Theoretical Physics, Johannes Guttenberg-UniversitätMathematical Sciences and STAG Research Centre, University of SouthamptonAbstract It is well-known that families of two-dimensional toroidal conformal field theories possess a dense subset of rational toroidal conformal field theories, which makes such families an interesting testing ground about rationality of conformal field theories in families in general. Rational toroidal conformal field theories possess an extended chiral and anti-chiral algebra known as W-algebras. Their partition functions decompose into a finite sum of products of holomorphic and anti-holomorphic characters of these W-algebras. Instead of considering these characters, we decompose the partition functions into products of characters of minimal extensions of u ̂ 1 $$ \hat{\mathfrak{u}}(1) $$ current algebras, which already appear for rational conformal field theories with target space S 1. We present an explicit construction that determines such decompositions. While these decompositions are not unique, they are universal in the sense that any rational toroidal conformal field theory with a target space torus of arbitrary dimension admits such decompositions. We illustrate these decompositions with a few representative examples of rational toroidal conformal field theories with two- and three-dimensional target space tori.https://doi.org/10.1007/JHEP07(2024)187Conformal Field Models in String TheoryScale and Conformal SymmetriesConformal and W SymmetryField Theories in Lower Dimensions |
| spellingShingle | Hans Jockers Maik Sarve Ida G. Zadeh Minimally extended current algebras of toroidal conformal field theories Journal of High Energy Physics Conformal Field Models in String Theory Scale and Conformal Symmetries Conformal and W Symmetry Field Theories in Lower Dimensions |
| title | Minimally extended current algebras of toroidal conformal field theories |
| title_full | Minimally extended current algebras of toroidal conformal field theories |
| title_fullStr | Minimally extended current algebras of toroidal conformal field theories |
| title_full_unstemmed | Minimally extended current algebras of toroidal conformal field theories |
| title_short | Minimally extended current algebras of toroidal conformal field theories |
| title_sort | minimally extended current algebras of toroidal conformal field theories |
| topic | Conformal Field Models in String Theory Scale and Conformal Symmetries Conformal and W Symmetry Field Theories in Lower Dimensions |
| url | https://doi.org/10.1007/JHEP07(2024)187 |
| work_keys_str_mv | AT hansjockers minimallyextendedcurrentalgebrasoftoroidalconformalfieldtheories AT maiksarve minimallyextendedcurrentalgebrasoftoroidalconformalfieldtheories AT idagzadeh minimallyextendedcurrentalgebrasoftoroidalconformalfieldtheories |