We review the relations between a family of domain-wall solutions to M-theory and gravitational instantons with special holonomy. When oxidized into the maximal-dimension parent supergravity, the transverse spaces of these domain walls become cohomogeneity-one spaces with generalized Heisenberg symmetries and a homoth-etic conformal symmetry. These metrics may also be obtained as scaling limits...

It is shown that several Hamiltonian systems possessing dynamical or hidden symmetries can be realized within the framework of Nambu’s generalized mechanics. Among such systems are the SU(n)-isotropic harmonic oscillator and the SO(4)-Kepler problem. As required by the formulation of Nambu dynamics, the integrals of motion for these systems necessarily become the so-called generalized Hamiltoni...

We demonstrate a universal mechanism of class instabilities in infrared regions for massless Abelian $p$-form gauge theories with topological interactions, which we call generalized chiral instabilities. Such occur the presence initial electric fields fields. show that dynamically generated magnetic tend to decrease and result configurations linking numbers, can be characterized by non-invertib...

Lagrangian symmetries and concomitant generalized Bianchi identities associated with the relabeling of fluid elements are found for hydrodynamics and magnetohydrodynamics (MHD). In hydrodynamics, relabeling results in Ertel's theorem of conservation of potential vorticity, while in MHD it yields the conservation of cross helicity. The symmetries of the reduction from Lagrangian (material) to Eu...

We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The method is then applied to the Schrödinger equation in order to obtain a realization of nonrelativistic quantum mechanics in discrete space–time. In this approach a quantum system on a lattice has a symmetry algebra iso...

We study the spectrum of bosonic strings in the light-like linear dilaton background and find discrete states. These are physical states which exist only at specific values of momentum. All except one discrete states generate spacetime symmetries. The exceptional discrete state corresponds to constraints which are deformations of conservation laws. The constraints resemble those arising from sy...