Related papers: Gauge Orbit Types for Theories with Classical Comp…
We consider faithful actions of simple algebraic groups on self-dual irreducible modules, and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the…
We begin the process of classifying all supersymmetric theories with quantum modified moduli. We determine all theories based on a single SU or Sp gauge group with quantum modified moduli. By flowing among theories we have calculated the…
We define gauge theories whose gauge group includes charge conjugation as well as standard $\mathrm{SU}(N)$ transformations. When combined, these transformations form a novel type of group with a semidirect product structure. For $N$ even,…
We present a group of transformations in the space of generalized connections that contains the set of transformations generated by the flux variables of loop quantum gravity. This group is labelled by certain SU(2)-valued functions on the…
A homogeneous Riemannian space $(M= G/H,g)$ is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group $G$. We study the structure of compact GO-spaces and give some…
We consider an SU(2)-lattice gauge model in the tree gauge. Classically, this is a system with symmetries whose configuration space is a direct product of copies of SU(2), acted upon by diagonal inner automorphisms. We derive defining…
We compute the mapping class group orbits in the homotopy set of framings of a compact connected oriented surface with non-empty boundary. In the case $g > 1$ the computation is some modification of Johnson's results and certain arguments…
By virtue of the well-known theorem, a structure Lie group K of a principal bundle $P$ is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K. In gauge theory, such sections are treated as Higgs…
Seiberg-like dualities in $2+1$d quiver gauge theories with $4$ supercharges are investigated. We consider quivers made of various combinations of classical gauge groups $U(N)$, $Sp(N)$, $SO(N)$ and $SU(N)$. Our main focus is the mapping of…
We introduce an elementary way of constructing principal (Z_2)^m-bundles over compact smooth manifolds. In addition, we will define a general notion of locally standard (Z_2)^m-actions on closed manifolds for all m>0, and then give a…
In this paper we study geodesics on adjoint orbits of $SL(n,\mathbb{R})$ equipped with $SO(n)$-invariant metrics (maximal compact subgroup). Our main technique is translate this problem into a geometric problem in the tangent bundle of…
Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups.…
Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…
Let $G$ be a connected reductive algebraic group over an algebraically closed field ${\bf k}$ of characteristic not equal to 2, let $\B$ be the variety of all Borel subgroups of $G$, and let $K$ be a symmetric subgroup of $G$. Fixing a…
The relation between manifold topology, observables and gauge group is clarified on the basis of the classification of the representations of the algebra of observables associated to positions and displacements on the manifold. The guiding,…
The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary…
Let F be the flag variety of a complex semi-simple group G, let H be an algebraic subgroup of G acting on F with finitely many orbits, and let V be an H-orbit closure in F. Expanding the cohomology class of V in the basis of Schubert…
The first part of this paper describes in detail the action of small gauge transformations in heterotic supergravity. We show a convenient gauge fixing is `holomorphic gauge' together with a condition on the holomorphic top form. This gauge…
Class lecture notes at a beginning graduate level on the mathematical background needed to understand classical gauge theory. Covers group actions, fiber bundles, principal bundles, connections, gauge transformations, parallel transport,…
By virtue of the well-known theorem, a structure Lie group G of a principal bundle P is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/H. In gauge theory, such sections are treated as classical…