T-duality in affine NA Toda models

The construction of non-Abelian affine Toda models is discussed in terms of its underlying Lie algebraic structure. It is shown that a subclass of such non-conformal two-dimensional integrable models naturally leads to the construction of a pair of actions, which share the same spectra and are related by canonical transformations.

The sl(2) affine Toda model coupled to the matter: solitons and confinement

The so-called conformal affine Toda theory coupled to the matter fields (CATM), associated to the (s) over capl(2) affine Lie algebra, is studied. The conformal symmetry is fixed by setting a connection to zero, then one defines an off-critical model, the affine Toda model coupled to the matter (ATM). Using the dressing transformation method we construct the explicit forms of the two-soliton classical solutions, and show that a physical bound soliton-antisoliton pair (breather) does not exist. Moreover, we verify that these solutions share some features of the sine-Gordon (massive Thirring) solitons, and satisfy the classical equivalence of topological and Noether currents in the ATM model. We show, using bosonization techniques that the ATM theory decouples into a sine-Gordon model and a free scalar. Imposing the Noether and topological currents equivalence as a constraint, one can show that the ATM model leads to a bag model like mechanism for the confinement of the color charge inside the sine-Gordon solitons (baryons).

Vertex operators and soliton solutions of affine Toda model with U(2) symmetry

The symmetry structure of the non-Abelian affine Toda model based on the coset SL(3)/SL(2) circle times U(1) is studied. It is shown that the model possess non-Abelian Noether symmetry closing into a q-deformed SL(2) circle times U(1) algebra. Specific two-vertex soliton solutions are constructed.

The Faddeev-Jackiw approach and the conformal affine sl(2) Toda model coupled to the matter field

The conformal affine sl(2) Toda model coupled to the matter field is treated as a constrained system in the context of Faddeev-Jackiw and the (constrained) symplectic schemes. We recover from this theory either the sine-Gordon or the massive Thirring model, through a process of Hamiltonian reduction, considering the equivalence of the Noether and topological currrents as a constraint and gauge fixing the conformal symmetry. (C) 2000 Academic Press.

Metric-affine approach to teleparallel gravity

The teleparallel gravity theory, treated physically as a gauge theory of translations, naturally represents a particular case of the most general gauge-theoretic model based on the general affine group of spacetime. on the other hand, geometrically, the Weitzenbock spacetime of distant parallelism is a particular case of the general metric-affine spacetime manifold. These physical and geometrical facts offer a new approach to teleparallelism. We present a systematic treatment of teleparallel gravity within the framework of the metric-affine theory. The symmetries, conservation laws and the field equations are consistently derived, and the physical consequences are discussed in detail. We demonstrate that the so-called teleparallel GR-equivalent model has a number of attractive features which distinguishes it among the general teleparallel theories, although it has a consistency problem when dealing with spinning matter sources.

Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Immersions in the metastable dimension range via the normal bordism approach

Let f : M --> N be a continuous map between two closed n-manifolds such that f(*): H-*(M, Z(2)) --> H-* (N, Z(2)) is an isomorphism. Suppose that M immerses in Rn+k for 5 less than or equal to n < 2k. Then N also immerses in Rn+k. We use techniques of normal bordism theory to prove this result and we show that for a large family of spaces we can replace the homolog condition by the corresponding one in homotopy. (C) 2001 Elsevier B.V. B.V. All rights reserved.

On codimensions k immersions of m-manifolds for k=1 and k=m-2

Let us consider M a closed smooth connected m-manifold, N a smooth ( 2m-2)-manifold and f: M -> N a continuous map, with m equivalent to 1( 4). We prove that if f*: H(1)(M; Z(2)) -> H(1)(f(M); Z(2)) is injective, then f is homotopic to an immersion. Also we give conditions to a map between manifolds of codimension one to be homotopic to an immersion. This work complements some results of Biasi et al. (Manu. Math. 104, 97-110, 2001; Koschorke in The singularity method and immersions of m-manifolds into manifolds of dimensions 2m-2, 2m-3 and 2m-4. Lecture Notes in Mathematics, vol. 1350. Springer, Heidelberg, 1988; Li and Li in Math. Proc. Camb. Phil. Soc. 112, 281-285, 1992).

THE CONSERVED CHARGES AND INTEGRABILITY OF THE CONFORMAL AFFINE TODA MODELS

We construct infinite sets of local conserved charges for the conformal affine Toda model. The technique involves the abelianization of the two-dimensional gauge potentials satisfying the zero-curvature form of the equations of motion. We find two infinite sets of chiral charges and apart from two lowest spin charges, all the remaining ones do not possess chiral densities. Charges of different chiralities Poisson commute among themselves. We discuss the algebraic properties of these charges and use the fundamental Poisson bracket relation to show that the charges conserved in time are in involution. Connections to other Toda models are established by taking particular limits.

Remarks on immersions in the metastable dimension range

In this work we present a generalization of an exact sequence of normal bordism groups given in a paper by H. A. Salomonsen (Math. Scand. 32 (1973), 87-111). This is applied to prove that if h : M-n --> Xn+k, 5 less than or equal to n < 2k, is a continuous map between two manifolds and g : M-n --> BO is the classifying map of the stable normal bundle of h such that (h, g)(*) : H-i (M, Z(2)) --> H-i (X x BO, Z(2)) is an isomorphism for i < n - k and an epimorphism for i = n - k, then h bordant to an immersion implies that h is homotopic to an immersion. The second remark complements the result of C. Biasi, D. L. Goncalves and A. K. M. Libardi (Topology Applic. 116 (2001), 293-303) and it concerns conditions for which there exist immersions in the metastable dimension range. Some applications and examples for the main results are also given.

An adaptation of the dual-affine interior point method for the surface flatness problem

This paper presents an adaptation of the dual-affine interior point method for the surface flatness problem. In order to determine how flat a surface is, one should find two parallel planes so that the surface is between them and they are as close together as possible. This problem is equivalent to the problem of solving inconsistent linear systems in terms of Tchebyshev's norm. An algorithm is proposed and results are presented and compared with others published in the literature. (C) 2006 Elsevier B.V. All rights reserved.

Higher spin symmetries and w∞ algebra in the conformal affine Toda model

As recently shown the conformal affine Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and -two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (w∞ algebra) is established.

Connection between the affine and conformal affine Toda models and their Hirota solution

It is shown that the affine Toda models (AT) constitute a gauge fixed version of the conformal affine Toda model (CAT). This result enables one to map every solution of the AT models into an infinite number of solutions of the corresponding CAT models, each one associated to a point of the orbit of the conformal group. The Hirota τ-functions are introduced and soliton solutions for the AT and CAT models associated to SL̂ (r+1) and SP̂ (r) are constructed.

Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra script Ĝ. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of script Ĝ, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.