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arXiv 1302.6645hep-lathep-phnucl-th
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从边界恢复手征对称性

Chiral Symmetry Restoration from a Boundary

B. C. Tiburzi

摘要:

流形的边界可以改变整体理论的相位。我们探讨了QCD的手征对称性的边界诱导相变的可能性。特别是,我们调查的后果强加齐次Dirichlet边界条件的夸克领域。这样的边界条件有时被用于格点规范理论计算中,例如,当包括外部电磁场时,或者当计算具有减少的时间范围的夸克传播子时。齐次Dirichlet边界条件迫使手征凝聚体在边界处消失,从而阻碍了体块中手征对称性的自发破缺。我们证明了由边界引起的手征对称性的恢复是一种依赖于自发对称性破缺机制的非微扰现象,并利用西格玛模型对这一问题进行了讨论.在这个模型中,我们发现,手征对称性是完全恢复,如果紧凑方向的长度小于2.0 fm。对于大于约4 μ m的长度,以致密方向的中点为中心形成近似均匀的手性缩合物。而体积平均凝聚体接近无穷大的体积值,紧凑的方向变得很长,有限尺寸的修正被证明是幂律,而不是指数。

英文摘要:

The boundary of a manifold can alter the phase of a theory in the bulk. We explore the possibility of a boundary-induced phase transition for the chiral symmetry of QCD. In particular, we investigate the consequences of imposing homogeneous Dirichlet boundary conditions on the quark fields. Such boundary conditions are sometimes employed in lattice gauge theory computations, for example, when including external electromagnetic fields, or when computing quark propagators with a reduced temporal extent. Homogeneous Dirichlet boundary conditions force the chiral condensate to vanish at the boundary, and thereby obstruct the spontaneous breaking of chiral symmetry in the bulk. We show the restoration of chiral symmetry due to a boundary is a non-perturbative phenomenon depending upon the mechanism of spontaneous symmetry breaking, and utilize the sigma model to exemplify the issues. Within this model, we find that chiral symmetry is completely restored if the length of the compact direction is less than 2.0 fm. For lengths greater than about 4 fm, an approximately uniform chiral condensate forms centered about the midpoint of the compact direction. While the volume-averaged condensate approaches the infinite volume value as the compact direction becomes very long, the finite-size corrections are shown to be power law rather than exponential.

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