Related papers: On Reconstructing Finite Gauge Group from Fusion R…
The locally BPS Wilson loop and the pure gauge Wilson loop map under AdS/CFT duality to string world-sheet boundaries with standard and alternate quantizations of the world-sheet fields. This implies an RG flow between the two operators,…
The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in ${\cal N}=4$ SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling…
We determine fusion rules (dimensions of the space of intertwining operators) among simple modules for the vertex operator algebra obtained as an even part of the symplectic fermionic vertex operator superalgebra. By using these fusion…
A recently proposed connection between closed string field and an open Wilson line defined on an arbitrary contour is further explored here. We suggest that reparametrization invariance of a Wilson line is the principle which determines the…
We prove that there is a finite level-independent bound on the number of relations defining the fusion ring of positive energy representations of the loop group of a simple, simply connected Lie group. As an illustration, we compute the…
I describe an application of Wilson Renormalization group to the real time formalism of finite temperature field theory. The approach has two nice features: 1) the RG flow equations describe non-perturbatively the effect of thermal…
A subgroup Q is commensurated in a group G if each G conjugate of Q intersects Q in a group that has finite index in both Q and the conjugate. So commensurated subgroups are similar to normal subgroups. Semistability and simple connectivity…
Quantum field theories can exhibit various generalized symmetry structures, among which higher-group symmetries and non-invertible symmetry defects are particularly prominent. In this work, we explore a new general scenario in which these…
The Tambara-Yamagami (TY) fusion category symmetry $\text{TY}(\mathbb{A},\chi,\epsilon)$ describes the enhanced non-invertible self-duality symmetry of a $2$-dim QFT under gauging a finite Abelian group $\mathbb{A}$. We generalize the…
Finite (or Discrete) Fourier Transforms (FFT) are essential tools in engineering disciplines based on signal transmission, which is the case in most of them. FFT are related with circulant matrices, which can be viewed as group matrices of…
We study junctions of Wilson lines in refined SU(N) Chern-Simons theory and their local relations. We focus on junctions of Wilson lines in antisymmetric and symmetric powers of the fundamental representation and propose a set of local…
We construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid given by the action of a finite group G on a space E. We…
A new approach is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the nowaday's standard…
We study the low-energy limit of Wilson lines (charged impurities) in conformal gauge theories in 2+1 and 3+1 dimensions. As a function of the representation of the Wilson line, certain defect operators can become marginal, leading to…
A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper we show how such gauge theories possess a higher-group global symmetry, which we study in detail. We derive the $d$-group…
It is well-known that if we gauge a $\mathbb{Z}_n$ symmetry in two dimensions, a dual $\mathbb{Z}_n$ symmetry appears, such that re-gauging this dual $\mathbb{Z}_n$ symmetry leads back to the original theory. We describe how this can be…
We give a general description of gauge symmetry breaking using vertical and remainder fluxes in 4D F-theory models. The fluxes can break a geometric gauge group to a smaller group and induce chiral matter, even when the larger group admits…
We derive a canonical form for 2-group gauge theory in 3+1D which shows they are either equivalent to Dijkgraaf-Witten theory or to the so-called "EF1" topological order of Lan-Wen. According to that classification, recently argued from a…
The Sylow graph $\Gamma(G)$ of a finite group $G$ originated from recent investigations on the so--called $\mathbf{N}$--closed classes of groups. The connectivity of $\Gamma(G)$ was proved only few years ago, involving the classification of…
We analyze loop-induced group-like symmetries in theories where fields are labeled by basis elements of a fusion algebra constructed from the conjugacy classes of finite groups. Although the fusion rules for conjugacy classes are in general…