The SCFT/VOA correspondence for twisted class S
<p>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 vertex algebras that have been given the moniker chiral algebras of class S. These vertex algebras are fascinating fro...
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| Format: | Thesis |
| Language: | English |
| Published: |
2023
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| _version_ | 1826312997653446656 |
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| author | Nair, SS |
| author2 | Beem, C |
| author_facet | Beem, C Nair, SS |
| author_sort | Nair, SS |
| collection | OXFORD |
| description | <p>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 vertex algebras that have been given the moniker chiral algebras of class S. These vertex algebras are fascinating from both a physical and mathematical point of view since they furnish novel representations of critical level affine Kac–Moody algebras. A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in [Ara18]. The construction 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 punctures that have been twisted by an outer automorphism of the Lie algebra.</p>
<p>In this thesis, we extend the construction of loc. cit. to theories of class S with twisted punctures. The resulting family of vertex algebras are, simultaneously, modules over two different critical level affine Kac–Moody algebras. We show that our proposal passes a number of consistency checks and establish results on gluing isomorphisms, and the action of generalised S-duality.</p> |
| first_indexed | 2024-09-25T04:03:59Z |
| format | Thesis |
| id | oxford-uuid:b7f8de8e-11e5-42ae-a40d-af6253c9a81e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:03:59Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | oxford-uuid:b7f8de8e-11e5-42ae-a40d-af6253c9a81e2024-05-14T11:32:57ZThe SCFT/VOA correspondence for twisted class SThesishttp://purl.org/coar/resource_type/c_db06uuid:b7f8de8e-11e5-42ae-a40d-af6253c9a81eMathematicsEnglishHyrax Deposit2023Nair, SSBeem, C<p>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 vertex algebras that have been given the moniker chiral algebras of class S. These vertex algebras are fascinating from both a physical and mathematical point of view since they furnish novel representations of critical level affine Kac–Moody algebras. A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in [Ara18]. The construction 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 punctures that have been twisted by an outer automorphism of the Lie algebra.</p> <p>In this thesis, we extend the construction of loc. cit. to theories of class S with twisted punctures. The resulting family of vertex algebras are, simultaneously, modules over two different critical level affine Kac–Moody algebras. We show that our proposal passes a number of consistency checks and establish results on gluing isomorphisms, and the action of generalised S-duality.</p> |
| spellingShingle | Mathematics Nair, SS The SCFT/VOA correspondence for twisted class S |
| title | The SCFT/VOA correspondence for twisted class S |
| title_full | The SCFT/VOA correspondence for twisted class S |
| title_fullStr | The SCFT/VOA correspondence for twisted class S |
| title_full_unstemmed | The SCFT/VOA correspondence for twisted class S |
| title_short | The SCFT/VOA correspondence for twisted class S |
| title_sort | scft voa correspondence for twisted class s |
| topic | Mathematics |
| work_keys_str_mv | AT nairss thescftvoacorrespondencefortwistedclasss AT nairss scftvoacorrespondencefortwistedclasss |