Integrability, Non-integrability and confinement

We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two approaches, the Form Factor Perturbation Theory and semiclassical methods. Each of them has its own advantage. Using the first approach, one can relate the confinement phenomena of topological excitations to the semi-locality of the operator which breaks integrability. Using the second approach, one can control the bound states which arise in each phase of the theory and predict that their number cannot be more than two.Comment: Invited talk at StatPhys24, Cairns (Australia) 2010. 27 pages, 16 figure

From spinons to magnons in explicit and spontaneously dimerized antiferromagnetic chains

We reconsider the excitation spectra of a dimerized and frustrated antiferromagnetic Heisenberg chain. This model is taken as the simpler example of compiting spontaneous and explicit dimerization relevant for Spin-Peierls compounds. The bosonized theory is a two frequency Sine-Gordon field theory. We analize the excitation spectrum by semiclassical methods. The elementary triplet excitation corresponds to an extended magnon whose radius diverge for vanishing dimerization. The internal oscilations of the magnon give rise to a series of excited state until another magnon is emited and a two magnon continuum is reached. We discuss, for weak dimerization, in which way the magnon forms as a result of a spinon-spinon interaction potential.Comment: 5 pages, latex, 3 figures embedded in the tex

Semiclassical methods in 2D QFT: spectra and finite-size effects

In this thesis, we describe some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques. These achievements represent a natural development of the non-perturbative studies performed in the past years for conformally invariant and integrable theories, which have led to analytical predictions for several measurable quantities in the universality classes of statistical systems. Here we propose a semiclassical method to control analytically the spectrum and the finite-size effects in both integrable and non-integrable theories. The techniques used are appropriate generalizations of the ones introduced in seminal works during the Seventies by Dashen, Hasslacher and Neveu and by Goldstone and Jackiw. Their approaches, which do not require integrability and therefore can be applied to a large class of systems, are best suited to deal with those quantum field theories characterized by a non-linear interaction potential with different degenerate minima. In fact, these systems display kink excitations which generally have a large mass in the small coupling regime. Under these circumstances, although the results obtained are based on a small coupling assumption, they are nevertheless non-perturbative, since the kink backgrounds around which the semiclassical expansion is performed are non-perturbative too.Comment: PhD thesis, 117 pages, 40 figure

Topological objects in QCD

Topological excitations are prominent candidates for explaining nonperturbative effects in QCD like confinement. In these lectures, I cover both formal treatments and applications of topological objects. The typical phenomena like BPS bounds, topology, the semiclassical approximation and chiral fermions are introduced by virtue of kinks. Then I proceed in higher dimensions with magnetic monopoles and instantons and special emphasis on calorons. Analytical aspects are discussed and an overview over models based on these objects as well as lattice results is given.Comment: 28 pages, 17 figures; Lectures given at 45th Internationale Universitaetswochen fuer Theoretische Physik (International University School of Theoretical Physics): Conceptual and Numerical Challenges in Femto- and Peta-Scale Physics, Schladming, Styria, Austria, 24 Feb - 3 Mar 200

On the integrability of two-dimensional models with U(1)xSU(N) symmetry

In this paper we study the integrability of a family of models with U(1)xSU(N) symmetry. They admit fermionic and bosonic formulations related through bosonization and subsequent T-duality. The fermionic theory is just the CP^(N-1) sigma model coupled to a self-interacting massless fermion, while the bosonic one defines a one-parameter deformation of the O(2N) sigma model. For N=2 the latter model is equivalent to the integrable deformation of the O(4) sigma model discovered by Wiegmann. At higher values of N we find that integrability is more sporadic and requires a fine-tuning of the parameters of the theory. A special case of our study is the N=4 model, which was found to describe the AdS_4xCP^3 string theory in the Alday-Maldacena decoupling limit. In this case we propose a set of asymptotic Bethe ansatz equations for the energy spectrum.Comment: 61 pages, 7 figure