Related papers: Higgs Branch and VOA of 4d $\mathcal{N}=2$ SCFTs f…
A well-developed classification program for 4d $\mathcal{N}=2$ super conformal field theories (SCFTs) leverages Seiberg-Witten geometry on the Coulomb branch of vacua; theories are arranged by increasing $\mathfrak{rank}$, the complex…
We build a bridge between two algebraic structures in SCFT: a VOA in the Schur sector of 4d $\mathcal{N}=2$ theories and an associative algebra in the Higgs sector of 3d $\mathcal{N}=4$. The natural setting is a 4d $\mathcal{N}=2$ SCFT…
We explore 3d $ \mathcal{N}=4 $ theories arising from twisted compactification of 4d $ \mathcal{N}=2 $ $ (G, G') $ Argyres-Douglas superconformal field theories (SCFTs), together with the 2d vertex operator algebras (VOAs) supported on the…
We propose a mirror symmetry for 4d $\mathcal{N}=2$ superconformal field theories (SCFTs) compactified on a circle with finite size. The mirror symmetry involves vertex operator algebra (VOA) describing the Schur sector (containing Higgs…
Vertex operator algebras (VOAs) arise in protected subsectors of supersymmetric quantum field theories, notably in 4d ${\mathcal N}=2$ superconformal field theories (SCFT) via the Schur sector and in twisted 3d ${\mathcal N}=4$ theories via…
Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant…
The Higgs branch of 4d $\mathcal{N}=2$ SCFTs can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class $\mathcal{S}$ theory corresponding to a genus-zero Riemann…
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 SCFT/VOA correspondence provides a powerful framework for studying 4d $\mathcal N=2$ superconformal field theories (SCFTs) through the mathematical machinery of 2d vertex operator algebras (VOAs). It captures the Schur operators of the…
We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type $J$ on a punctured sphere. We denote the AD theories as $(J^b[k],Y)$, where $J^b[k]$ and…
We start with the SCFT/VOA correspondence formulated in the Omega-background approach, and connect it to the boundary VOA in 3d $\mathcal{N}=4$ theories and chiral algebras of 2d $\mathcal{N}=(0,2)$ theories. This is done using 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…
We analyze the N=2 superconformal field theories that arise when a pair of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we…
We detail the Higgs branches of 6d $(1,0)$ superconformal field theories (SCFTs) and little string theories (LSTs) that exhibit supersymmetry-enhancing Higgs branch renormalization group flows to the 6d $(2,0)$ SCFTs and LSTs of type DE.…
There is a well-known map from 4d $\mathcal{N}=2$ superconformal field theories (SCFTs) to 2d vertex operator algebras (VOAs). The 4d Schur index corresponds to the VOA vacuum character, and must be a solution with integral coefficients of…
Every four-dimensional ${\cal N}=2$ superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator algebra. The relationships between this invariant and more conventional protected…
We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the $W$ algebra defined using nilpotent orbit with partition $[q^m,1^s]$. Gauging above AD…
We present free field realizations for the associated vertex operator algebras of a number of four-dimensional $\mathcal{N}=2$ superconformal field theories. Our constructions utilize an exceptionally small set of chiral bosons whose number…
Detailed studies of four dimensional N=2 superconformal field theories (SCFT) defined by isolated complete intersection singularities are performed: we compute the Coulomb branch spectrum, Seiberg-Witten solutions and central charges. Most…
We classify rank zero 5d SCFTs geometrically engineered from M-theory on quasi-homogeneous compound Du Val isolated threefold singularities. For all such theories, we characterize the Higgs Branch, by computing the dimension, the continuous…