相关论文: 3d mirror symmetry of braided tensor categories

We study the simplest example of mirror symmetry for 3d $\mathcal N=4$ SUSY gauge theories: the A-twist of a free hypermultiplet and the B-twist of SQED. We particularly focus on the category of line operators in each theory. Using the work…

We prove the Kazhdan-Lusztig correspondence for a class of vertex operator superalgebras which, via the work of Costello-Gaiotto, arise as boundary VOAs of topological B twist of 3d $\mathcal{N}=4$ abelian gauge theories. This means that we…

By a pointed vertex operator algebra (VOA) we mean one whose modules are all simple currents (i.e. invertible), e.g. lattice VOAs. This paper systematically explores the interplay between their orbifolds and tensor category theory. We begin…

We study properties of vertex (operator) algebras associated with 3d H-twisted $\mathcal{N}=4$ supersymmetric gauge theories with a boundary. The vertex operator algebras (VOAs) are defined by BRST cohomologies of currents with symplectic…

We initiate the study of boundary Vertex Operator Algebras (VOAs) of topologically twisted 3d $\mathcal{N}=4$ rank-0 SCFTs. This is a recently introduced class of $\mathcal{N}=4$ SCFTs that by definition have zero-dimensional Higgs and…

We introduce two mirror constructions of Vertex Operator Algebras associated to special boundary conditions in 3d N=4 gauge theories. We conjecture various relations between these boundary VOA's and properties of the (topologically twisted)…

In this paper, we study the structure of a general framed vertex operator algebra. We show that the structure codes (C,D) of a framed VOA V satisfy certain duality conditions. As a consequence, we prove that every framed VOA is a simple…

Let $V$ be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure. We prove that the…

We study Vertex Operator Algebras (VOAs) obtained from the H-twist of 3d $\mathcal{N}=4$ linear quiver gauge theories. We find that H-twisted VOAs can be regarded as the ''chiralization'' of the extended Higgs branch: many of the…

Using the tensor category theory developed by Lepowsky, Zhang and the second author, we construct a braided tensor category structure with a twist on a semisimple category of modules for an affine Lie algebra at an admissible level. We…

We show that if $V$ is a vertex operator algebra such that all the irreducible ordinary $V$-modules are $C_1$-cofinite and all the grading-restricted generalized Verma modules for $V$ are of finite length, then the category of finite length…

We study the 2D vertex operator algebra (VOA) construction in 4D $\mathcal{N}=2$ superconformal field theories (SCFT) on $S^3 \times S^1$, focusing both on old puzzles as well as new observations. The VOA lives on a two-torus…

The anomaly of non-invertible higher-form symmetries is determined by the braiding of topological operators implementing them. In this paper, we study a method to classify braidings on topological line and surface operators by leveraging…

We introduce a category B of bounded modules for the toroidal Lie algebras and study irreducible modules in B. We show that one of the irreducible modules in this category, L(T_0), admits a structure of a vertex operator algebra. We prove…

We study half-BPS line operators in 3d N=4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic types of such line operators, distinguished by the SUSY…

The correspondence between four-dimensional $\mathcal{N}=2$ superconformal field theories and vertex operator algebras, when applied to theories of class $\mathcal{S}$, leads to a rich family of VOAs that have been given the monicker chiral…

We establish braided tensor equivalences among module categories over the twisted quantum double of a finite group defined by an extension of a group H by an abelian group, with 3-cocycle inflated from a 3-cocycle on H. We also prove that…

Suppose $V^G$ is the fixed-point vertex operator subalgebra of a compact group $G$ acting on a simple abelian intertwining algebra $V$. We show that if all irreducible $V^G$-modules contained in $V$ live in some braided tensor category of…

Prototypical rational vertex operator algebras are associated to affine Lie algebras at positive integer level k. They correspond physically to the Wess-Zumino-Witten theories, and their representation theory can be captured by quantum…

We describe the topological $A$ and $B$ twists of 3d $\mathcal{N}=4$ theories of hypermultiplets gauged by $\mathcal{N}=4$ vector multiplets as certain deformations of the holomorphic-topological ($HT$) twist of those theories, utilizing…