Related papers: Nonabelian dualization of plane wave backgrounds
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…
The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators. The system is superintegrable and its symmetry generators…
We develop new mathematical tools for the study of the double copy and colour-kinematics duality for tree-level scattering amplitudes using the properties of Lie polynomials. We show that the $S$-map that was defined to simplify…
Hopf algebra quantizations of 4-dimensional and 6-dimensional real classical Drinfel'd doubles are studied by following a direct "analytic" approach. The full quantization is explicitly obtained for most of the Drinfel'd doubles, except a…
The identification between the complex plane and the Riemann sphere preserves holomorphic and harmonic functions and is a classical tool. In this paper we consider a similar mapping from an unbounded metric space $X$ to a bounded space and…
Starting from a consistency requirement between T-duality symmetry and renormalization group flows, the two-loop metric beta function is found for a d=2 bosonic sigma model on a generic, torsionless background. The result is obtained…
An example of the holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity theories is found. The constraints on the target space geometry of the 4d, N=2 non-linear sigma-models in N=2…
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries…
We show how to implement T-duality along non-abelian isometries in backgrounds with non-vanishing Ramond fields. When the dimension of the isometry group is odd (even) the duality swaps (preserves) the chirality of the theory. In certain…
The correspondence between Poisson homogeneous spaces over a Poisson-Lie group $G$ and Lagrangian Lie subalgebras of the classical double $D({\mathfrak g})$ is revisited and explored in detail for the case in which ${\mathfrak…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
We will consider the high frequency behaviour of distorted plane waves on manifolds of nonpositive curvature which are Euclidean or hyperbolic near infinity, under the assumption that the curvature is negative close to the trapped set of…
Harnessing the unimodular degree of freedom in the definition of any toric diagram, we present a method of constructing inequivalent gauge theories which are world-volume theories of D-branes probing the same toric singularity. These…
Geometric structures and dualities arise naturally in quantum field theories and string theory. In fact, these tools become very useful when studying strong coupling effects, where standard perturbative techniques can no longer be used. In…
The gauge symmetry and shift/translational symmetry of a 3D BF action, which are associated to a pair of dual Lie algebras, can be combined to form the Drinfel'd double. This combined symmetry is the gauge symmetry of the Chern-Simons…
Kontsevich's formality theorem states that the differential graded Lie algebra of multidifferential operators on a manifold M is L-infinity-quasi-isomorphic to its cohomology. The construction of the L-infinity map is given in terms of…
We explicitly determine the group of isomorphism classes of equivariant line bundles on the non-archimedean Drinfeld upper half plane for $\mathrm{GL}_2(F)$, for its subgroups of matrices whose determinant has even (respectively trivial)…
Non-Abelian duality transformations built on non-semi-simple isometry groups are analysed. We first give the conditions under which the original non-linear sigma model and its non-Abelian dual are equivalent. The existence of an invariant…
We extend the recent result of T.Tao to wave maps defined from the Minkowski space of dimension >4 to a target Riemannian manifold which possesses a ``bounded parallelizable'' structure. This is the case of Lie groups, homogeneous spaces as…
Duality properties of the $SU(2)$ Principal Chiral Model are investigated starting from a one-parameter family of its equivalent Hamiltonian descriptions generated by a non-Abelian deformation of the cotangent space $T^*SU(2) \simeq SU(2)…