3D mirror symmetry and the βγ VOA

Ballin, Andrew; Niu, Wen‐Jun

doi:10.1142/s0219199722500699

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…We have a few series of examples in mind, see also Example 2.12. There is one relatively straight forward example related to physics, namely certain categories of line operators in twists of three dimensional abelian N = 4 supersymmetric gauge theories are realized by braided tensor categories of VOAs that are extensions of several singlet and Heisenberg algebras [BCDN23] and so via uprolling the corresponding quantum groups can and will be constructed and their connection to the gauge theory should then also further be investigated. The other examples are ambitious programs that we are truely excited about.…”

Section: Discussionmentioning

confidence: 99%

A Kazhdan–Lusztig Correspondence for $$L_{-\frac{3}{2}}(\mathfrak {sl}_3)$$

Creutzig

Ridout

Rupert

2023

Commun. Math. Phys.

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Let U be a braided tensor category, typically unknown, complicated and in particular non-semisimple. We characterize U under the assumption that there exists a commutative algebra A in U with certain properties: Let C be the category of local A-modules in U and B the category of A-modules in U, which are in our set-up usually much simpler categories than U. Then we can characterize U as a relative Drinfeld center Z C (B) and B as representations of a certain Hopf algebra inside C.In particular this allows us to reduce braided tensor equivalences to the knowledge of abelian equivalences, e.g. if we already know that U is abelian equivalent to the category of modules of some quantum group U q or some generalization thereof, and if C is braided equivalent to a category of graded vector spaces, and if A has a certain form, then we already obtain a braided tensor equivalence between U and Rep(U q ).A main application of our theory is to prove logarithmic Kazhdan-Lusztig correspondences, that is, equivalences of braided tensor categories of representations of vertex algebras and of quantum groups. Here, the algebra A and the corresponding category C are a-priori given by a free-field realization of the vertex algebra and by a Nichols algebra. We illustrate this in those examples where the representation theory of the vertex algebra is well enough understood. In particular we prove the conjectured correspondences between the singlet vertex algebra M(p) and the unrolled small quantum groups of sl 2 at 2p-th root of unity. Another new example is the Kazhdan-Lusztig correspondence between the affine vertex algebra of gl 1|1 and an unrolled quantum group of gl 1|1 . * this should be q = exp πi r ∨ (k+h ∨ ) with h ∨ the dual Coxeter number of g and r ∨ the lacing number of the even subalgebra.

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Section: Discussionmentioning

confidence: 99%

A Kazhdan–Lusztig Correspondence for $$L_{-\frac{3}{2}}(\mathfrak {sl}_3)$$

Creutzig

Ridout

Rupert

2023

Commun. Math. Phys.

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“…More generally, if B is an abelian current, then there is a family of automorphism of its mode algebra that sends B → B + λ z ; if this is a current subalgebra of a larger vertex algebra V, it need not lift to an automorphism of all of V, cf. section 2.4 of [34]. For example, if O ∈ V is a current JHEP08(2023)088 algebra primary of weight q then we need λq ∈ Z.…”

Section: Boundary Monopoles In Abelian Gauge Theories and Spectral Flowmentioning

confidence: 99%

“…See e.g. [34][35][36] for examples of how this process can be implemented in more interesting examples; the work [35] studies the algebra of local operators on a Dirichlet boundary condition in the (topological) B-twist of 3d N = 4 SQED, whereas the more recent [34,36] apply these same techniques to study yet more involved abelian N = 4 gauge theories. The much earlier work [37] studies related simple current extensions from a purely VOA perspective.…”

Section: Boundary Monopoles In Abelian Gauge Theories and Spectral Flowmentioning

confidence: 99%

Twistorial monopoles & chiral algebras

Garner,

Paquette

2023

J. High Energ. Phys.

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We initiate the study of how the insertion of magnetically charged states in 4d self-dual gauge theories impacts the 2d chiral algebras supported on the celestial sphere at asymptotic null infinity, from the point of view of the 4d/2d twistorial correspondence introduced by Costello and the second author. By reducing the 6d twistorial theory to a 3d holomorphic-topological theory with suitable boundary conditions, we can motivate certain non-perturbative enhancements of the celestial chiral algebra corresponding to extensions by modules arising from 3d boundary monopole operators. We also identify the insertion of 4d (non-abelian) monopoles with families of spectral flow automorphisms of the celestial chiral algebra.

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