Harold Blas

Non-commutative solitons and strong-weak duality

Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either U(1) ? U(1) or U(1)C corresponding to the Lechtenfeld et al. (NCSG1) or Grisaru-Penati (NCSG2) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT1,2 models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM1,2 models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter ? for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG1 NCMT1 is promising since it is expected to hold on the quantum level.

Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory

The solitons and kinks of the generalized sl(3,) sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the tau functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions, and the soliton masses formulae. As a reduced submodel we obtain the double sine-Gordon model. Moreover, we provide the algebraic construction of the sl(3,) affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized sl(3,) sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U(1) vector and topological currents it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for ``quark confinement.

Exotic baryons in two-dimensional QCD and the generalized sine-Gordon solitons

The solitons and kinks of the SU(3) generalized sine-Gordon model (GSG) are shown to describe the baryonic spectrum of two-dimensional quantum chromodynamics (QCD2). The GSG model arises in the low-energy effective action of bosonized QCD2 with unequal quark mass parameters. The GSG potential for Nf = 3 flavors resembles the potential of the effective chiral lagrangian proposed by Witten to describe low-energy behavior of four dimensional QCD. Among the attractive features of the GSG model are the variety of soliton and kink type solutions for QCD2 unequal quark mass parameters [JHEP(0701)(2007)(027)]. Exotic baryons in QCD2 [J. Ellis et al JHEP0508(2005)081] are discussed in the context of the GSG model. Various semi-classical computations are performed improving the results of this reference and clarifying the role of unequal quark masses. The remarkable double sine Gordon model also arises as a reduced GSG model bearing a kink(K) type solution describing a multi-baryon; so, the description of some resonances in QCD2 may take advantage of the properties of the K system.

Bosonization and generalized Mandelstam soliton operators

Abstract.The generalized massive Thirring model (GMT) with three fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with three interacting soliton species. The generalized Mandelstam soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive-definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. In the semi-classical limit one recovers the so-called SU(3) affine Toda model coupled to matter fields (ATM) from which the classical GSG and GMT models were recently derived in the literature. The intermediate ATM-like effective action possesses some spinors resembling the higher grading fields of the ATM theory which have non-zero chirality. These fields are shown to disappear from the physical spectrum, thus providing a bag-model-like confinement mechanism and leading to the appearance of massive fermions (solitons). The ordinary MT/SG duality turns out to be related to each SU(2) sub-group. The higher rank Lie algebra extension is also discussed.

Bosonized noncommutative bi-fundamental fermion and S-duality

We perform the path-integral bosonization of the recently proposed noncommutative massive Thirring model (NCMT1) [JHEP 0503 (2005) 037]. This model presents two types of current-current interaction terms related to the bi-fundamental representation of the group U(1). Firstly, we address the bosonization of a bi-fundamental free Dirac fermion defined on a noncommutative (NC) euclidean plane θ2. In this case we show that the fermion system is dual to two copies of the NC Wess-Zumino-Novikov-Witten model. Next, we apply the bosonization prescription to the NCMT1 model living on θ2 and show that this model is equivalent to two-copies of the WZNW model and a two-field potential defined for scalar fields corresponding to the global U(1) × U(1) symmetry plus additional bosonized terms for the four fermion interactions. The bosonic sector resembles to the one proposed by Lechtenfeld et al. [Nucl. Phys. B 705 (2005) 477] as the noncommutative sine-Gordon for a pair of scalar fields. The bosonic and fermionic couplings are related by a strong-weak duality. We show that the couplings of the both sectors for some representations satisfy similar relationships up to relevant re-scalings, thus the NC bi-fundamental couplings are two times the corresponding ones of the NC fundamental (anti-fundamental) and eight times the couplings of the ordinary massive Thirring and sine-Gordon models.

Spatial shifts of colliding dark solitons in deformed non-linear Schrödinger models

We derive a closed expression for the spatial shift experienced by a black soliton colliding with a shallow dark soliton in the context of deformed nonlinear Schrodinger (NLS) models. A perturbative scheme is developed based on the expansion parameter , where v is the velocity of the incoming shallow dark soliton, and vs is the Bogoliubov sound speed, therefore it is not restricted to small deformations of the integrable NLS model. As applications of our formalism we consider the integrable NLS model and the non-integrable cubic-quintic NLS model with non-vanishing boundary conditions. Extensive numerical simulations are performed in order to verify our results. A variant of the analysis for gray–gray soliton collision is discussed regarding a fast broad soliton and a slow thin soliton.

Quasi-integrability in the modified defocusing non-linear Schrödinger model and dark solitons

A bstractThe concept of quasi-integrability has been examined in the context of deformations of the defocusing non-linear Schrödinger model (NLS). Our results show that the quasi-integrability concept, recently discussed in the context of deformations of the sine-Gordon, Bullough-Dodd and focusing NLS models, holds for the modified defocusing NLS model with dark soliton solutions and it exhibits the new feature of an infinite sequence of alternating conserved and asymptotically conserved charges. For the special case of two dark soliton solutions, where the field components are eigenstates of a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved in the scattering process of the solitons. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. We perform extensive numerical simulations and consider the scattering of dark solitons for the cubic-quintic NLS model with potential V=ηI2−∈6I3

Quasi-integrable non-linear Schrödinger models, infinite towers of exactly conserved charges and bright solitons

V=\eta {I}^2-\frac{\in }{6}{I}^3