Related papers: On $\mathbb{Z}/2\mathbb{Z}$ permutation gauging
Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data - S, T and fusion matrices - are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain…
The aim of these lectures is to describe a construction, as self-contained as possible, of renormalized gauge theories. Following a suggestion of Polchinski, we base our analysis on the Wilson renormalization group method. After a…
We investigate a relationship between a particular class of two-dimensional integrable non-linear $\sigma$-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the $\lambda$-deformed $G/G$…
We compute all fusion algebras with symmetric rational $S$-matrix up to dimension 12. Only two of them may be used as $S$-matrices in a modular datum: the $S$-matrices of the quantum doubles of $\mathbb{Z}/2\mathbb{Z}$ and $S_3$. Almost all…
We consider a formulation of Yang-Mills theory where the gauge field is valued on an octonionic algebra and the gauge transformation is the group of automorphisms of it. We show, under mild assumptions, that the only possible gauge…
Zagier proved that the generating series for the traces of singular moduli is a \textit{weakly holomorphic} modular form of weight 3/2 on $\Gamma_0(4)$. Bruinier and Funke extended the results of Zagier to modular curves of arbitrary genus.…
We study a 4d gauge theory $U(1)^{N-1}\rtimes S_N$ obtained from a $U(1)^{N-1}$ theory by gauging a 0-form symmetry $S_N$. We show that this theory has a global continuous 2-category symmetry, whose structure is particularly rich for $N>2$.…
For a reductive group $G$, Harder-Narasimhan theory gives a structure theorem for principal $G$ bundles on a smooth projective curve $C$. A bundle is either semistable, or it admits a canonical parabolic reduction whose associated Levi…
We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)/Z_2, which possesses nontrivial topology. In particular, there are…
This paper is the second part of the series "Spherical higher order Fourier analysis over finite fields", aiming to develop the higher order Fourier analysis method along spheres over finite fields, and to solve the geometric Ramsey…
The Poisson gauge algebra is a semi-classical limit of complete non-commutative gauge algebra. In the present work we formulate the Poisson gauge theory which is a dynamical field theoretical model having the Poisson gauge algebra as a…
In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick up on Wiles' work and generalize the numerical criterion to…
A method developed by Polychronakos to study singular gauge transformations in 1+2 dimensional non-commutative Chern-Simons gauge theory is generalized from U(1) group to U(2) group. The method clarifies the singular behavior of…
The problem of determining gauge and monoidal equivalence classes of fusion categories is considered from the perspective of geometric invariant theory. It is shown that the gauge (or monoidal) class of a fusion category is determined by…
It is shown that non-commutative spaces, which are quotients of associative algebras by ideals generated by non-linear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of…
We propose a way to introduce matter fields transforming in arbitrary representations of the gauge group in noncommutative U(N) gauge theories. We then argue that in the presence of supersymmetry, an ordinary commutative SU(N) gauge theory…
Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which…
In standard quantum field theory, the one-particle states are classified by the unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite-dimensional (non-unitary) representations of the…
We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible…
The gauge principle is proposed for rigid Lie-groupoidal symmetries $G=>M$ of the Polyakov-Alvarez-Gaw\k{e}dzki 2$d$ non-linear $\sigma$-model with metric target $(M,g_M)$ and the WZ term given by a CS differential character coming from an…