arXiv 0907.03802009-07-02hep-th

2维胶子凝聚的不对称性：零温度情形

The asymmetry of the dimension 2 gluon condensate: the zero temperature case

D. Dudal, J. A. Gracey, N. Vandersickel, D. Vercauteren, H. Verschelde

备注：: 25 pages
发表信息：: Phys.Rev.D80:065017,2009
DOI：: 10.1103/PhysRevD.80.065017

摘要：

本文给出了局部复合算子A_μA_v-δ_{μ v}/dA^2和A^2的代数研究，其中d=4是时空维。我们证明，这些是单独重整化的所有订单在朗道规范。这对应于算子A_μA_v到它的迹和无迹部分的可重整化分解。我们提出了明确的结果，相关的重整化群函数的三个循环的顺序，伴随着这些结果的各种测试。然后，我们发展了一种形式来确定相应凝聚体的零温有效势，并恢复了已知的<A^2> \neq 0的结果，以及<A_μA_v-δ_{μ v}/d A^2>=0，这是一个非平凡的检验，证明了该方法与洛伦兹对称性是一致的。这种形式很容易推广到有限温度的情况，这将使未来对<A^2>凝聚体的电磁对称性进行分析研究成为可能，这一点从最近由Aldudub和Ilgenfritz进行的晶格模拟中得到了有力的证据，他们将他们的结果与杨-米尔斯相图中的3个区域联系起来。

英文摘要：

We provide an algebraic study of the local composite operators A_μA_ν-δ_{μν}/d A^2 and A^2, with d=4 the spacetime dimension. We prove that these are separately renormalizable to all orders in the Landau gauge. This corresponds to a renormalizable decomposition of the operator A_μA_νinto its trace and traceless part. We present explicit results for the relevant renormalization group functions to three loop order, accompanied with various tests of these results. We then develop a formalism to determine the zero temperature effective potential for the corresponding condensates, and recover the already known result for <A^2> \neq 0, together with <A_μA_ν-δ_{μν}/d A^2>=0, a nontrivial check that the approach is consistent with Lorentz symmetry. The formalism is such that it is readily generalizable to the finite temperature case, which shall allow a future analytical study of the electric-magnetic symmetry of the <A^2> condensate, which received strong evidence from recent lattice simulations by Chernodub and Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase diagram.

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英文摘要：

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