arXiv 0709.36672007-09-23hep-th

广义sine-Gordon模型与二维QCD中的重子

Generalized sine-Gordon model and baryons in two-dimensional QCD

Harold Blas

备注：: 45 pages. Latex. To appear as a chapter of the book 'High Energy Physics Research Advances', Nova Science publishers

摘要：

考虑sl（3，C）仿射Toda模型与物质（Dirac旋量）（ATM）的耦合，通过规范固定过程，得到了完全由Dirac旋量耦合的广义sl（3，C）sine-Gordon模型（cGSG）的经典形式. GSG模型是普通sine-Gordon模型的多场扩展。在旋量部分，我们只剩下狄拉克场与CGSG场的耦合。基于U（1）矢量和拓扑流之间的等价性，证明了cGSG模型中的孤子和扭结中旋量的禁闭，为“夸克”禁闭提供了一个扩展的强子模型[JHEP 0701（2007）027]。此外，广义sine-Gordon（GSG）模型的孤子和扭结被用来描述二维QCD的正常和奇异重子谱。GSG模型产生于具有不等夸克质量参数的玻色化QCD 2的低能有效作用量[JHEP 0703（2007）055]。三种味的GSG势类似于Witten提出的描述四维QCD低能行为的有效手征拉格朗日势。在GSG模型的吸引人的特点是各种各样的孤子和扭结型解的QCD 2不等夸克质量参数。QCD 2中的奇异重子[ Ellis and Frishman，JHEP 0508（2005）081]在GSG模型的背景下讨论。各种半经典计算进行改进以前的结果和澄清不等夸克质量的作用。著名的双正弦戈登模型也是一个简化的GSG模型，它有一个描述多重子的扭结（K）型解。

英文摘要：

We consider 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. The GSG models are multifield extensions of the ordinary sine-Gordon model. 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, which holds in the theory, 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 [JHEP0701(2007)027]. Moreover, the solitons and kinks of the generalized sine-Gordon (GSG) model are shown to describe the normal and exotic baryon spectrum of two-dimensional QCD. The GSG model arises in the low-energy effective action of bosonized QCD2 with unequal quark mass parameters [JHEP0703(2007)055]. The GSG potential for three 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. Exotic baryons in QCD2 [ Ellis and Frishman, JHEP0508(2005)081] are discussed in the context of the GSG model. Various semi-classical computations are performed improving previous results 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.

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