We show that if r ≥ 3 and α is a faithful Z-Cartan action on a torus T by automorphisms, then any closed subset of (T) which is invariant and topologically transitive under the diagonal Z-action by α is homogeneous, in the sense that it is either the full torus (T), or a finite set of rational points, or a finite disjoint union of parallel translates of some d-dimensional invariant subtorus. A ...

Talk given at the 2nd Topical Meeting on Constrained Dynamics and Quantum Gravity, Santa Margherita, Ligure, Italy, 17-21 September, 1996. To be published in the proceedings (Editor: V. de Alfaro). OUTP-96-72P hep-th/9701161 December 1996 (1) is only diffeomorphism-invariant. This reflects the presence of an anomaly, i.e. the fact that there are no path-integral measures with invariance under b...

We show that the class of functions of topologically nontrivial gauge transformations in QCD includes a zero-mode of the Gauss law constraint. The equivalent unconstrained system compatible with Feynman's integral is derived in terms of topological invariant variables, where the zero-mode is identified with the winding number collective variable and leads to the dominance of the Wu-Yang monopol...

We study toroidal orbifold models with topologically invariant terms in the path integral formalism and give physical interpretations of the terms from an operator formalism point of view. We briefly discuss a possibility of a new class of modular invariant orbifold models. Work supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (No.3018381...

The non-abelian self-dual action in three dimensions is derived using the self-interaction mechanism. Self-duality in three dimensions was proposed initially by Townsend et. al. [1] as an alternative to the topologically massive theory[2]. In principle, they seem different descriptions of a locally massive spin 1 physical excitation: the self-dual theory is described by a non-gauge invariant fi...

The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

Topological entanglement entropy is a topological invariant which can detect topological order of quantum many-body ground state. We assume an existence of such order parameter at finite temperature which is invariant under smooth deformation of the subsystems, and study its stability under hamiltonian perturbation. We apply this assumption to a Gibbs state of hamiltonian which satisfies so cal...

We present a topological description of the quantum spin-Hall effect (QSHE) in a two-dimensional electron system on a honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be characterized by a 2 x 2 matrix of first Chern integers. The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern num...

We study a non-Hermitian Kitaev chain model that contains three sources of non-Hermiticity: constant imaginary potential, asymmetry between hopping amplitudes $t_{\rm R}$ and L}$ in the right left directions, imbalance pair potentials $\Delta_{\rm c}$ a}$ for creation annihilation, respectively. show bulk--boundary correspondence holds this system; two topological invariants defined bulk geomet...

We present a simple, computation free and geometrical proof of the following classical result: for a diffeomorphism of a manifold, any compact submanifold which is invariant and normally hyperbolic persists under small perturbations of the diffeomorphism. The persistence of a Lipschitz invariant submanifold follows from an application of the Schauder fixed point theorem to a graph transform, wh...