Related papers: 't Hooft tensor for generic gauge group
As a color confinement mechanism, a dual Meissner effect due to Abelian monopoles involved in QCD has been discussed so far in various ways. But still there is an important problem unsolved. It is gauge invariance of the schemes or, in…
We apply gauge theory to study the space $F_k(M)$ of smooth codimension-$k$ framed foliations on a smooth manifold $M$. The quotient of Maurer-Cartan elements by the action of an infinite dimensional non-abelian gauge groupoid forms a…
Let $Y$ be a pointed space and let $\mathcal E(Y^r)$ be the group of based self-equivalences of $Y^r$, $r\geq 2$. For $Y$ a homotopy commutative $H$-group we construct a subgroup $\mathcal E_{\mathrm{Mat}}(Y^r)$ of $\mathcal E(Y^r)$ which…
A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology theory representable in the motivic stable homotopy category…
We study 't Hooft lines and the associated $\mathcal{L}$- operators in topological 4D Chern-Simons theory with gauge symmetry given by the exceptional groups E$_{6}$ and E$_{7}$. We give their oscillator realisations and propose topological…
Monopole bubbling effect is screening of magnetic charges of singular Dirac monopoles by regular 't Hooft-Polyakov monopoles. We study properties of weak coupling perturbative series in the presence of monopole bubbling effects as well as…
Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…
The method of quantization of magnetic monopoles based on the order-disorder duality existing between the monopole operator and the lagrangian fields is applied to the description of the quantum magnetic monopoles of `t Hooft and Polyakov…
Recent progress in the construction of both electric, coloured and magnetic charges in gauge theories will be presented. The topological properties of the charged sectors will be highlighted as well as the applications of this work to…
We give a definition of differentiable cohomology of a Lie group G (possibly infinite-dimensional) with coefficients in any abelian Lie group. This differentiable cohomology maps both to the cohomology of the group made discrete and to Lie…
Let $T$ be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf{Mod}(T)$ to be homotopically equivalent to $\mathbb{CP}^\infty$. In particular,…
We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We…
We propose to use the different kinds of vacua of the gauge theories coupled to matter as a laboratory to test confinement ideas of pure Yang-Mills theories. In particular, the very poor overlap of the Wilson loop with the broken string…
Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group $G$, we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded…
Homotopy Lie algebras are a generalization of differential graded Lie algebras encoding both the kinematics and dynamics of a given field theory. Focusing on kinematics, we show that these algebras provide a natural framework for the…
By considering singular gauge transformations of the five-dimensional Hedge-Hog monopole, we obtain a class of multi-charged Tchrakian monopoles. The charge is classified by the fourth homotopy group of SU(4)/U(1)xSU(2)xSU(2).
By making use of the decomposition theory of gauge potential, the inner structure of SU(2) and SO(4) gauge theory is discussed in detail. We find the SO(4) monopole can be given via projecting the SO(4) gauge field onto an antisymmetric…
We study gauge properties of the general teleparallel theory of gravity, defined in the framework of Poincare gauge theory. It is found that the general theory is characterized by two kinds of gauge symmetries: a specific gauge symmetry…
We construct a generalization of pure lattice gauge theory (LGT) where the role of the gauge group is played by a tensor category. The type of tensor category admissible (spherical, ribbon, symmetric) depends on the dimension of the…
We investigate the Higgs mechanism for gravity, which has been recently put forward by 't Hooft, when the Polyakov-type action for scalar fields is added to the original action. We find that from the Polyakov-type action, it is very natural…