Related papers: Study of a lattice 2-group gauge model
We introduce a self-dual field strength which replaces the gauge field in spontaneously broken Yang-Mills theory, reformulating it as a Lorentz covariant non-linear sigma model. This dualized theory is in both a unitary and renormalizable…
A complexification of the twisted $\N=2$ theory allows one to determine the N=4 Yang--Mills theory in its third twist formulation. The imaginary part of the gauge symmetry is used to eliminate two scalars fields and create gauge covariant…
We discuss two dimensional Yang -- Mills theories with massless fermions in arbitrary representations of a gauge group $G$. It is shown that the physics (spectrum and interactions) of the massive states in such models is independent of the…
We construct the lattice gauge theory of the group G_N, the semidirect product of the permutation group S_N with U(1)^N, on an arbitrary Riemann surface. This theory describes the branched coverings of a two-dimensional target surface by…
In this article we analyze the vacuum structure of pure SU(2) Yang-Mills using non-perturbative techniques. Monte Carlo simulations are performed for the lattice gauge theory with external sources to obtain the effective potential. Evidence…
In this series of papers, we study a Hamiltonian model for 3+1d topological phases, based on a generalisation of lattice gauge theory known as "higher lattice gauge theory". Higher lattice gauge theory has so called "2-gauge fields"…
We study a duality transformation from the gauge-invariant subspace of a $\mathbb{Z}_N$ lattice gauge theory on a two-leg ladder geometry to an $N$-clock model on a single chain. The main feature of this mapping is the emergence of a…
We apply quantum group methods for noncommutative geometry to the $Z_2\times Z_2$ lattice to obtain a natural Dirac operator on this discrete space. This then leads to an interpretation of the Higgs fields as the discrete part of spacetime…
Fracton theories possess exponentially degenerate ground states, excitations with restricted mobility, and nontopological higher-form symmetries. This paper shows that such theories can be defined on arbitrary spatial lattices in three…
We study the mixed topological / holomorphic Chern-Simons theory of Costello, Witten and Yamazaki on an orbifold $(\Sigma\times{\mathbb C})/{\mathbb Z}_2$, obtaining a description of lattice integrable systems in the presence of a boundary.…
The construction of non-Abelian Euclidean Yang-Mills theories in dimension four, as scaling limits of lattice Yang-Mills theories or otherwise, is a central open question of mathematical physics. This paper takes the following small step…
We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree…
We consider purely topological $2$d Yang-Mills theory on a torus with the second Stiefel-Whitney class added to the Lagrangian in the form of a $\theta$-term. It will be shown, that at $\theta=\pi$ there exists a class of $SU(2…
We argue that a simple qubit-regularized $\mathrm{SU}(2)$ lattice gauge theory (LGT) on a plaquette chain serves as a pseudo-one-dimensional toy model for Yang-Mills (YM) theory in three spatial dimensions. We map the chain Hamiltonian to…
New clues for the best understanding of the nature of the symmetry-breaking mechanism are revealed in this paper. A revision of the standard gauge transformation properties of Yang-Mills fields, according to a group approach to quantization…
We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.
Dual superconductivity is believed to be a promising mechanism for quark confinement and has been investigated on a lattice effectively by a particular gauge called the maximal Abelian (MA) gauge. We propose a new formulation of SU(3)…
This brief review surveys recent progress driven by the gauge/Yang-Baxter equation (YBE) correspondence. This connection has proven to be a powerful tool for discovering novel integrable lattice spin models in statistical mechanics by…
A first-order, confinement/deconfinement phase transition appears in the finite temperature behavior of many non-Abelian gauge theories. These theories play an important role in proposals for completion of the Standard Model of particle…
We discuss a new approach for putting gauge theories on the lattice. The gauge fields are defined on the lattice only, but are interpolated to the interior of the lattice cells, where they couple to continuum fermions. The purpose of this…