相关论文: Defect groups of class $\mathcal{S}$ theories from…

We formulate a conjectural relation between the category of line defects in topologically twisted 3d ${\cal N} = 4$ supersymmetric quantum field theories and categories of modules for Vertex Operator Algebras of boundary local operators for…

Six-dimensional superconformal field theories (SCFTs) give rise to four-dimensional (4d) ones when compactified on Riemann surfaces. In the $\mathcal{N}=(2,0)$ case, this yields the famous class S family. For $\mathcal{N}=(1,0)$ theories…

We study surface defects in 4d $\mathcal{N}=1$ $SU(N)$ superconformal gauge theories of class $\mathcal{S}_k$ obtained from the 6d (1,0) theories of type $A_{N-1}$, which are worldvolume theories on $N$ M5-branes at…

We study a large class of BPS surface defects in 4d N=2 gauge theories. They are defined by coupling a 2d N=(2,2) gauged linear sigma model to the 4d bulk degrees of freedom. Our main result is an efficient computation of the effective…

We study BPS line defects in N=2 supersymmetric four-dimensional field theories. We focus on theories of "quiver type," those for which the BPS particle spectrum can be computed using quiver quantum mechanics. For a wide class of models,…

It is known that some theories of class $S$ are actually factorized into multiple decoupled nontrivial four-dimensional $N=2$ theories. We propose a way of constructing examples of this phenomenon using the physics of half-BPS surface…

A relative theory is a boundary condition of a higher-dimensional topological quantum field theory (TQFT), and carries a non-trivial defect group formed by mutually non-local defects living in the relative theory. Prime examples are 6d…

2-group symmetries are generalized symmetries that arise when 1-form and 0-form symmetries mix with each other. We uncover the existence of a class of 2-group symmetries in general 4d N=2 theories of Class S that can be constructed by…

We study the local properties of a class of codimension-2 defects of the 6d N=(2,0) theories of type J=A,D,E labeled by nilpotent orbits of a Lie algebra \mathfrak{g}, where \mathfrak{g} is determined by J and the outer-automorphism twist…

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 use the F-theory realization of 6D superconformal field theories (SCFTs) to study the corresponding spectrum of stringlike, i.e. surface defects. On the tensor branch, all of the stringlike excitations pick up a finite tension, and there…

With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class $\mathcal{S}_{\Gamma}$. The class $\mathcal{S}_{\Gamma}$ theories arise from M5-branes probing…

The BPS spectrum of certain N=2 supersymmetric field theories can be determined algebraically by studying the representation theory of BPS quivers. We introduce methods based on BPS quivers to study line defects. The presence of a line…

Coulomb branches of vacua are the most universal moduli spaces that arise in local unitary interacting 4d $\mathcal{N}=2$ superconformal field theories (SCFTs). In these theories, $1/2$-BPS primaries parameterize the Coulomb branches and…

We study generalized global symmetries and their 't Hooft anomalies in 3d N=4 superconformal field theories (SCFTs). Following some general considerations, we focus on good quiver gauge theories, comprised of balanced unitary nodes and…

Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a monoidal category of BPS line defects. Any Coulomb vacuum of such a theory can be conjecturally associated to an ``algebra of BPS…

We study the Coulomb branches of the rank-one 4d $\mathcal{N} = 2$ quantum field theories, including the KK theories obtained from the circle compactification of the 5d $\mathcal{N}= 1$ $E_n$ Seiberg theories. The focus is set on the…

In the context of class S theories and 4D/2D duality relations there, we discuss the skein relations of general topological defects on the 2D side which are expected to be counterparts of composite surface-line operators in 4D class S…

We conjecture a formula for the Schur index of four-dimensional $\mathcal{N}=2$ theories coupled to $(2,2)$ surface defects in terms of the $2d$-$4d$ BPS spectrum in the Coulomb phase of the theory. The key ingredient in our conjecture is a…

We study the regular surface defect in the Omega-deformed four-dimensional supersymmetric gauge theory with gauge group SU(N) with 2N hypermultiplets in fundamental representation. We prove its vacuum expectation value obeys the…