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

Abstract

The solitons and kinks of the generalized sl(3,C) 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,C) 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,C) 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.

Renormalization of QCD2

“…The difference between the bosonized models appears when N f > 2 and N c > 2. We note that the low energy multi-flavor QCD 2 with unequal masses can also be bosonized giving a so called generalized SG model [10,26] but its investigation is out of the scope of this paper.…”

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

“…This model corresponds to the generalized sine-Gordon model (GSG) recently studied in the context of the bosonization of the so-called generalized massive Thirring model (GMT) with N f fermion species [19,20,22]. The classical GSG model and some of its properties, such as the algebraic construction based on the affine sl(n,C) Kac-Moody algebra and the soliton spectrum has been the subject of a recent paper [21].…”

“…The GSG model has appeared in the study of the strong coupling sector of the sl(n,C) ATM theory [19,20,21], and in the bosonized multiflavor massive Thirring model [22]. In particular, the GSG model provides the framework to obtain (multi-)soliton solutions for unequal quark mass parameters.…”

“…Here we summarize some properties of the sl(3,C) GSG model [21,22] relevant to our discussions above, such as the soliton and kink spectrum. The discussions make some connection to the QCD 2 developments above, such as (multi-) baryon number of solitons and kinks.…”

An investigation of the Casimir energy for a fermion coupled to the sine-Gordon soliton with parity decomposition

“…This has motivated us to investigate this coupled fermion-soliton model with the sine-Gordon soliton as a prescribed background field. Amongst solitonic models, sine-Gordon model enjoys a special status due to its intrinsic richness and wide range of applications in several areas including QCD [65,66] and condensed matter physics [67]. Since 1958, much work has been done to phenomenologically describe hadrons and their interactions using nonlinear field theory [68].…”