Gluing vertex algebras

Creutzig, Thomas; Kanade, Shashank; McRae, Robert

doi:10.1016/j.aim.2021.108174

Cited by 27 publications

(31 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular the category of λ-twisted modules for generic λ is semisimple with We observe that this coincides with the counting of Bethe roots in T A n,k , as in (4.52), (5.51). Note that the conjecture follows from work in progress [267] for the case g = sl 2 (see Example 2 of Section 6.5.2). In this case all λ ∈ S 1 \ {1} are generic.…”

Section: Modules In the Presence Of Abelian Flat Connectionsmentioning

confidence: 98%

“…If (and conjecturally also only if) there is indeed a braid-reversed equivalence between the finite tensor categories of two VOA's, then these two VOA's can be extended to a VOA with trivial module category (e.g. free fermions), and the extension is exactly of the form (6.91)-(6.92) by [164]. In the case of sl (2) we are able to perform branching-rule computations that nicely support our conjecture.…”

Section: In Particular We Will Prove Thatmentioning

confidence: 99%

“…We seem to encounter a similar subtlety when seeking a level-rank duality involving FT k (sl n ) and N n,k . In fact, whenever one has a mutually commuting pair of VOAs inside a VOA with trivial representation category (like the free fermions) and certain technical vertex tensor category assumptions are satisfied then one has a braid-reversed equivalence of categories of modules of the two VOAs [164].…”

Section: "Level-rank" Dualitymentioning

confidence: 99%

See 2 more Smart Citations

A QFT for non-semisimple TQFT

Creutzig¹,

Dimofte²,

Garner³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We construct a family of 3d quantum field theories T A n,k that conjecturally provide a physical realization -and derived generalization -of non-semisimple mathematical TQFT's based on the modules for the quantum group U q (sl n ) at an even root of unity q = exp(iπ/k). The theories T A n,k are defined as topological twists of certain 3d N = 4 Chern-Simons-matter theories, which also admit string/M-theory realizations. They may be thought of as SU (n) k−n Chern-Simons theories, coupled to a twisted N = 4 matter sector (the source of non-semisimplicity). We show that T A n,k admits holomorphic boundary conditions supporting two different logarithmic vertex operator algebras, one of which is an sl n -type Feigin-Tipunin algebra; and we conjecture that these two vertex operator algebras are related by a novel logarithmic level-rank duality. (We perform detailed computations to support the conjecture.) We thus relate the category of line operators in T A n,k to the derived category of modules for a boundary Feigin-Tipunin algebra, and -using a logarithmic Kazhdan-Lusztiglike correspondence that has been established for n = 2 and expected for general n -to the derived category of U q (sl n ) modules. We analyze many other key features of T A n,k and match them from quantum-group and VOA perspectives, including deformations by flat P GL(n, C) connections, one-form symmetries, and indices of (derived) genus-g state spaces.

show abstract

Section: Modules In the Presence Of Abelian Flat Connectionsmentioning

confidence: 98%

Section: In Particular We Will Prove Thatmentioning

confidence: 99%

Section: "Level-rank" Dualitymentioning

confidence: 99%

See 1 more Smart Citation

A QFT for non-semisimple TQFT

Creutzig¹,

Dimofte²,

Garner³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let V 1 and V 25 be the (simple) Virasoro vertex operator algebras of central charge 1 and 25, respectively. In this final section, we use the gluing construction of [CKM2] to obtain a new vertex algebra extension of V 1 ⊗ V 25 . This extension is a conformal vertex algebra in the sense of [HLZ1], since it has a conformal vector but infinite-dimensional conformal weight spaces.…”

Section: Gluing Virasoro Vertex Algebrasmentioning

confidence: 99%

“…Thus O 0 1 and O 0 25 are braid-reversed equivalent. A consequence of this result, via the method of gluing vertex algebras [CKM2], is a simple conformal vertex algebra structure on the 'modified regular representation of the Virasoro algebra' associated to the central charge pair (1,25). This algebra extends V 1 ⊗ V 25 and is analogous to the conformal vertex algebras of central charge 26 constructed in [FS,FZ2] as extensions of tensor products of Virasoro vertex operator algebras at central charge 13 ± 6t ± 6t −1 , t / ∈ Q.…”

Section: Introductionmentioning

confidence: 96%

An $\mathfrak{sl}_2$-type tensor category for the Virasoro algebra at central charge $25$ and applications

McRae¹,

Yang²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Let O25 be the vertex algebraic braided tensor category of finite-length modules for the Virasoro Lie algebra at central charge 25 whose composition factors are the irreducible quotients of reducible Verma modules. We show that O25 is rigid and that its simple objects generate a semisimple tensor subcategory that is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional sl2-modules. We also show that this sl2type subcategory is braid-reversed tensor equivalent to a similar category for the Virasoro algebra at central charge 1. As an application, we obtain a new conformal vertex algebra of central charge 26 as an extension of the tensor product of Virasoro vertex operator algebras at central charges 1 and 25, analogous to the modified regular representations of the Virasoro algebra constructed previously from Virasoro vertex operator algebras at generic central charges by I. Frenkel-Styrkas and I. Frenkel-M. Zhu.

show abstract

An $$\mathfrak {sl}_2$$-type tensor category for the Virasoro algebra at central charge 25 and applications

McRae

Yang

2023

Math. Z.

View full text Add to dashboard Cite

Gluing vertex algebras

Cited by 27 publications

References 47 publications

A QFT for non-semisimple TQFT

A QFT for non-semisimple TQFT

An $\mathfrak{sl}_2$-type tensor category for the Virasoro algebra at central charge $25$ and applications

An $$\mathfrak {sl}_2$$-type tensor category for the Virasoro algebra at central charge 25 and applications

Contact Info

Product

Resources

About