arXiv 1104.22362011-04-12nucl-thhep-ph

大N_c QCD中有限密度下的手征对称性恢复

On Chiral Symmetry Restoration at Finite Density in Large N_c QCD

Thomas D. Cohen, Prabal Adhikari, Mark C. Strother, Raja R. M. Ayyagari

备注：: 12 pages, 1 table
发表信息：: Phys.Rev.C83:065201,2011
DOI：: 10.1103/PhysRevC.83.065201

摘要：

在N_c较大时，冷核物质将形成晶体，从而自发地破坏平移对称性。对手征对称性破缺和平移对称性破缺的描述可能会交织在一起。在这里，重点是手征对称性破缺和可能的恢复，是由建设独立的平移对称性破缺的性质-即手性序参量的空间平均数方面。如果所有空间平均手性序参量为零，则认为系统是手性恢复的。一个关键的问题是，在这个意义上的手征恢复是可能的相位，其中手征序参量是局部非零，但其空间平均值都消失。我们表明，这是不可能的，除非所有的手征不变的观测空间均匀。这一结果首先来自Skyrme型模型，这是基于一个非线性西格玛模型和建设打破手征对称性上逐点的基础上。手征恢复（在平均意义上）的所有模型，这种类型的一个不去定理，得到通过显示，在这些模型中存在手征对称的序参量，不能空间均匀。其次，我们证明了no-go定理适用于任何相位的大N_c QCD，它具有非零但空间变化的手征凝聚。该定理证明，在一个假定的手征恢复阶段，字段配置可以减少到一个非线性西格玛模型。

英文摘要：

At large N_c, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is on aspects of chiral symmetry breaking and its possible restoration that are by construction independent of the nature of translational symmetry breaking---namely spatial averages of chiral order parameters. A system will be considered to be chirally restored provided all spatially-averaged chiral order parameters are zero. A critical question is whether chiral restoration in this sense is possible for phases in which chiral order parameters are locally non-zero but whose spatial averages all vanish. We show that this is not possible unless all chirally-invariant observables are spatially uniform. This result is first derived for Skyrme-type models, which are based on a nonlinear sigma model and by construction break chiral symmetry on a point-by-point basis. A no-go theorem for chiral restoration (in the average sense) for all models of this type is obtained by showing that in these models there exist chirally symmetric order parameters which cannot be spatially uniform. Next we show that the no-go theorem applies to large N_c QCD in any phase which has a non-zero but spatially varying chiral condensate. The theorem is demonstrated by showing that in a putative chirally-restored phase, the field configuration can be reduced to that of a nonlinear sigma model.

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