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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Yazar: Nair, SS
Diğer Yazarlar: Beem, C
Materyal Türü: Tez
Dil:English
Baskı/Yayın Bilgisi: 2023
Konular:
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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>
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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