Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model

The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $\sigma$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the spectral density scaling hypothesis. The resulting approximation to the spin--spin correlation function agrees well with that computed in renormalized (asymptotically free) perturbation theory in the expected energy range. Further we observe simple lower and upper bounds for the sum of the absolute square of the form factors which may be of use for analytic estimates.Comment: 14 pages, 3 figures, late

On symmetries of Chern-Simons and BF topological theories

We describe constructing solutions of the field equations of Chern-Simons and topological BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations) are considered. A method of calculating (nonlocal) dressing symmetries in Chern-Simons and topological BF theories is formulated

On anomalies in classical dynamical systems

The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamiltonian formulation admits symmetries of the action for which the Noether conserved charges, endorsed with the Poisson bracket structure, close an algebra which is just the centrally extended version of the original symmetry algebra. The consistency conditions for this to occur are derived. Explicit examples are given based on simple two-dimensional models. Applications of the above scheme and lines of further investigations are suggested.Comment: arXiv version is already officia

R-matrix Quantization of the Elliptic Ruijsenaars--Schneider model

It is shown that the classical L-operator algebra of the elliptic Ruijsenaars-Schneider model can be realized as a subalgebra of the algebra of functions on the cotangent bundle over the centrally extended current group in two dimensions. It is governed by two dynamical r and $\bar{r}$-matrices satisfying a closed system of equations. The corresponding quantum R and $\overline{R}$-matrices are found as solutions to quantum analogs of these equations. We present the quantum L-operator algebra and show that the system of equations on R and $\overline{R}$ arises as the compatibility condition for this algebra. It turns out that the R-matrix is twist-equivalent to the Felder elliptic R^F-matrix with $\overline{R}$ playing the role of the twist. The simplest representation of the quantum L-operator algebra corresponding to the elliptic Ruijsenaars-Schneider model is obtained. The connection of the quantum L-operator algebra to the fundamental relation RLL=LLR with Belavin's elliptic R matrix is established. As a byproduct of our construction, we find a new N-parameter elliptic solution to the classical Yang-Baxter equation.Comment: latex, 29 pages, some misprints are corrected and the meromorphic version of the quantum L-operator algebra is discusse

Integrable mixing of A_{n-1} type vertex models

Given a family of monodromy matrices {T_u; u=0,1,...,K-1} corresponding to integrable anisotropic vertex models of A_{(n_u)-1}-type, we build up a related mixed vertex model by means of glueing the lattices on which they are defined, in such a way that integrability property is preserved. Algebraically, the glueing process is implemented through one dimensional representations of rectangular matrix algebras A(R_p,R_q), namely, the `glueing matrices' zeta_u. Here R_n indicates the Yang-Baxter operator associated to the standard Hopf algebra deformation of the simple Lie algebra A_{n-1}. We show there exists a pseudovacuum subspace with respect to which algebraic Bethe ansatz can be applied. For each pseudovacuum vector we have a set of nested Bethe ansatz equations identical to the ones corresponding to an A_{m-1} quasi-periodic model, with m equal to the minimal range of involved glueing matrices.Comment: REVTeX 28 pages. Here we complete the proof of integrability for mixed vertex models as defined in the first versio

Integrability in Theories with Local U(1) Gauge Symmetry

Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1) generalization of the standard strong and weak constraints for models with two dimensional target space. The Bogomolny sector is discussed, as well, and we find that each Bogomolny configuration supports infinitely many conserved currents. Finally, other models with U(1) gauge symmetry are investigated.Comment: corrected typos, version accepted in J. Phys.

The Geometrodynamics of Sine-Gordon Solitons

The relationship between N-soliton solutions to the Euclidean sine-Gordon equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is investigated, with emphasis on the important role played by the dilaton in determining the black hole geometry. We show how an N-soliton solution can be used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and construct the transformation to more standard ``Schwarzchild-like'' coordinates. For N=1 and 2, we find explicit closed form solutions to the dilaton equations of motion in soliton coordinates, and find the relationship between the soliton parameters and the black hole mass. Remarkably, the black hole mass is non-negative for arbitrary soliton parameters. In the one-soliton case the coordinates are shown to cover smoothly a region containing the whole interior of the black hole as well as a finite neighbourhood outside the horizon. A Hamiltonian analysis is performed for slicings that approach the soliton coordinates on the interior, and it is shown that there is no boundary contribution from the interior. Finally we speculate on the sine-Gordon solitonic origin of black hole statistical mechanics.Comment: Latex, uses epsf, 30 pages, 6 figures include

Gauge-Invariant Coordinates on Gauge-Theory Orbit Space

A gauge-invariant field is found which describes physical configurations, i.e. gauge orbits, of non-Abelian gauge theories. This is accomplished with non-Abelian generalizations of the Poincare'-Hodge formula for one-forms. In a particular sense, the new field is dual to the gauge field. Using this field as a coordinate, the metric and intrinsic curvature are discussed for Yang-Mills orbit space for the (2+1)- and (3+1)-dimensional cases. The sectional, Ricci and scalar curvatures are all formally non-negative. An expression for the new field in terms of the Yang-Mills connection is found in 2+1 dimensions. The measure on Schroedinger wave functionals is found in both 2+1 and 3+1 dimensions; in the former case, it resembles Karabali, Kim and Nair's measure. We briefly discuss the form of the Hamiltonian in terms of the dual field and comment on how this is relevant to the mass gap for both the (2+1)- and (3+1)-dimensional cases.Comment: Typos corrected, more about the non-Abelian decomposition and inner products, more discussion of the mass gap in 3+1 dimensions. Now 23 page

Chern-Simons Field Theories with Non-semisimple Gauge Group of Symmetry

Subject of this work is a class of Chern-Simons field theories with non-semisimple gauge group, which may well be considered as the most straightforward generalization of an Abelian Chern-Simons field theory. As a matter of fact these theories, which are characterized by a non-semisimple group of gauge symmetry, have cubic interactions like those of non-abelian Chern-Simons field theories, but are free from radiative corrections. Moreover, at the tree level in the perturbative expansion,there are only two connected tree diagrams, corresponding to the propagator and to the three vertex originating from the cubic interaction terms. For such theories it is derived here a set of BRST invariant observables, which lead to metric independent amplitudes. The vacuum expectation values of these observables can be computed exactly. From their expressions it is possible to isolate the Gauss linking number and an invariant of the Milnor type, which describes the topological relations among three or more closed curves.Comment: 16 pages, 1 figure, plain LaTeX + psfig.st

On the determinant representations of Gaudin models' scalar products and form factors

We propose alternative determinant representations of certain form factors and scalar products of states in rational Gaudin models realized in terms of compact spins. We use alternative pseudo-vacuums to write overlaps in terms of partition functions with domain wall boundary conditions. Contrarily to Slavnovs determinant formulas, this construction does not require that any of the involved states be solutions to the Bethe equations; a fact that could prove useful in certain non-equilibrium problems. Moreover, by using an atypical determinant representation of the partition functions, we propose expressions for the local spin raising and lowering operators form factors which only depend on the eigenvalues of the conserved charges. These eigenvalues define eigenstates via solutions of a system of quadratic equations instead of the usual Bethe equations. Consequently, the current work allows important simplifications to numerical procedures addressing decoherence in Gaudin models.Comment: 15 pages, 0 figures, Published versio