Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing
The correspondence between four-dimensional N=2 superconformal field theories and vertex operator algebras, when applied to theories of class S, leads to a rich family of VOAs that have been given the monicker chiral algebras of class S. A remarkably uniform construction of these vertex operator alg...
| المؤلفون الرئيسيون: | , |
|---|---|
| التنسيق: | Journal article |
| اللغة: | English |
| منشور في: |
Springer
2022
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| _version_ | 1826309573817925632 |
|---|---|
| author | Beem, C Nair, S |
| author_facet | Beem, C Nair, S |
| author_sort | Beem, C |
| collection | OXFORD |
| description | The correspondence between four-dimensional N=2 superconformal field theories and vertex operator algebras, when applied to theories of class S, leads to a rich family of VOAs that have been given the monicker chiral algebras of class S. A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in Arakawa (Chiral algebras of class S and Moore–Tachikawa symplectic varieties, 2018. arXiv:1811.01577 [math.RT]). The construction of Arakawa (2018) takes as input a choice of simple Lie algebra g, and applies equally well regardless of whether g is simply laced or not. In the non-simply laced case, however, the resulting VOAs do not correspond in any clear way to known four-dimensional theories. On the other hand, the standard realisation of class S theories involving non-simply laced symmetry algebras requires the inclusion of outer automorphism twist lines, and this requires a further development of the approach of Arakawa (2018). In this paper, we give an account of those further developments and propose definitions of most chiral algebras of class S with outer automorphism twist lines. We show that our definition passes some consistency checks and point out some important open problems. |
| first_indexed | 2024-03-07T07:37:48Z |
| format | Journal article |
| id | oxford-uuid:50e8940a-edce-4ec7-acd4-67b1dd6f6f76 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:37:48Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:50e8940a-edce-4ec7-acd4-67b1dd6f6f762023-03-30T09:09:12ZTwisted chiral algebras of class S and mixed Feigin-Frenkel gluingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:50e8940a-edce-4ec7-acd4-67b1dd6f6f76EnglishSymplectic ElementsSpringer2022Beem, CNair, SThe correspondence between four-dimensional N=2 superconformal field theories and vertex operator algebras, when applied to theories of class S, leads to a rich family of VOAs that have been given the monicker chiral algebras of class S. A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in Arakawa (Chiral algebras of class S and Moore–Tachikawa symplectic varieties, 2018. arXiv:1811.01577 [math.RT]). The construction of Arakawa (2018) takes as input a choice of simple Lie algebra g, and applies equally well regardless of whether g is simply laced or not. In the non-simply laced case, however, the resulting VOAs do not correspond in any clear way to known four-dimensional theories. On the other hand, the standard realisation of class S theories involving non-simply laced symmetry algebras requires the inclusion of outer automorphism twist lines, and this requires a further development of the approach of Arakawa (2018). In this paper, we give an account of those further developments and propose definitions of most chiral algebras of class S with outer automorphism twist lines. We show that our definition passes some consistency checks and point out some important open problems. |
| spellingShingle | Beem, C Nair, S Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing |
| title | Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing |
| title_full | Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing |
| title_fullStr | Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing |
| title_full_unstemmed | Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing |
| title_short | Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing |
| title_sort | twisted chiral algebras of class s and mixed feigin frenkel gluing |
| work_keys_str_mv | AT beemc twistedchiralalgebrasofclasssandmixedfeiginfrenkelgluing AT nairs twistedchiralalgebrasofclasssandmixedfeiginfrenkelgluing |