Related papers: Gauging C on the Lattice
We discuss a particular lattice discretization of abelian gauge theories in arbitrary dimensions. The construction is based on gauging the center symmetry of a non-compact abelian gauge theory, which results in a Villain type action. We…
We discuss U(1) lattice gauge theory models based on a modified Villain formulation of the gauge action, which allows coupling to bosonic electric and magnetic matter. The formulation enjoys a duality which maps electric and magnetic…
A generalization of Wilsonian lattice gauge theory may be obtained by considering the possible self-adjoint extensions of the electric field operator in the Hamiltonian formalism. In the special case of 3D $\mathrm{U}(1)$ gauge theory these…
We construct Villain Hamiltonians for compact scalars and abelian gauge theories. The Villain integers are promoted to integral spectrum operators, whose canonical conjugates are naturally compact scalars. Further, depending on the theory,…
Based on the Ginsparg-Wilson relation, a gauge invariant formulation of electroweak SU(2)xU(1) gauge theory on the lattice is considered. If the hypercharge gauge coupling is turned off in the vacuum sector of the U(1) gauge fields, the…
In $U(1)$ lattice gauge theory with compact $U(1)$ variables, we construct the symmetry operator, i.e.\ the topological defect, for the axial $U(1)$ noninvertible symmetry. This requires a lattice formulation of chiral gauge theory with an…
We study how the symmetry operator of the axial $U(1)$ non-invertible symmetry acts on the 't~Hooft line operator in the $U(1)$ gauge theory by employing the modified Villain-type lattice formulation. We model the axial anomaly by a compact…
In this work we realize the 3 + 1 dimensional non-invertible ${\mathbb{Z}}_N$ chiral symmetry generator as an operator in a many body lattice Hilbert space. A crucial ingredient in our construction is the use of infinite dimensional $U(1)$…
We introduce a method to investigate the static and dynamic properties of both Abelian and non-Abelian lattice gauge models in 1+1 dimensions. Specifically, we identify a set of transformations that disentangle different degrees of freedom,…
Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is \emph{exactly\/}…
We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces…
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive…
We study a recently proposed formulation of U(1) lattice field theory with electric and magnetic matter based on the Villain formulation. This discretization allows for a duality that gives rise to relations between weak and strong gauge…
The U(N) gauge theory on a D-dimensional lattice is reformulated as a theory of lattice strings (a statistical model of random surfaces). The Boltzmann weights of the surfaces can have both signs and are tuned so that the longitudinal modes…
We present a new family of gauge invariant non-local order parameters for (non-abelian) discrete gauge theories on a Euclidean lattice, which are in one-to-one correspondence with the excitation spectrum that follows from the representation…
In this contribution we revisit the lattice discretization of the topological charge for abelian lattice field theories. The construction departs from an initially non-compact discretization of the gauge fields and after absorbing $2\pi$…
We construct two-dimensional ${\cal N} = (2, 2)$ supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU($N_c$) color group. These lattice theories…
We study a 3d lattice gauge theory with gauge group $\mathrm{U}(1)^{N-1}\rtimes \mathrm{S}_N$, which is obtained by gauging the $\mathrm{S}_N$ global symmetry of a pure $\mathrm{U}(1)^{N-1}$ gauge theory, and we call it the semi-Abelian…
In this paper we present results of numerical simulations and some (analytical) approximations of a compact $U(1)\ltimes\ZZ_2$ lattice gauge theory, including an extra bare mass term for Alice fluxes. The subtle interplay between Alice…
We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry.…