arXiv 1007.47202010-07hep-lathep-th

D=3+1 SU（N）规范理论中的闭合通量管及其弦描述

Closed flux tubes and their string description in D=3+1 SU(N) gauge theories

Andreas Athenodorou, Barak Bringoltz, Michael Teper

备注：: 65 pages, 22 figures; more on massive modes, minor corrections, recent references added
发表信息：: JHEP 1102:030,2011
DOI：: 10.1007/JHEP02(2011)030

摘要：

我们计算了封闭在空间圆环周围的约束通量管的能谱，作为其长度l的函数。我们对3+1维中的各种SU（N）规范理论，以及各种自旋、宇称和纵向动量值都是这样做的。我们能够给出大约20个最轻的这种状态的有用的精确结果，对于l的范围，从接近（有限体积）退细化相变开始，一直延伸到l.sqrt（K）~6（其中K是弦张力）。我们发现这些低能级中的大多数都可以用平坦时空中的Nambu-Goto自由弦论的谱来描述。值得注意的是，这不仅是在较大的l值，在那里基态能量和低激发之间的间隙与质量间隙相比变得很小，而且在更短的长度上，这些激发能与sqrt（K）相比变得很大，通量管不再“看起来"像一根细弦，并且有效弦作用量以1/l的幂的展开不再收敛。所有这一切都是为了基本表象中的通量。我们还计算了k=2（反对）对称基态，这些结果表明在小的l.到目前为止，所有这些都与我们先前在2+1维中的发现非常相似。然而，与D=2+1的情况相反，我们还发现有一些态，J，P=0，-量子数，显示出与Nambu-Goto谱的较大偏差。我们调查的可能性，（一些）这些国家可能编码的大规模模式与内部结构的通量管，我们讨论了如何早熟的自由弦行为的大多数国家约束的有效字符串行动，最近取得了许多有趣的理论进展。

英文摘要：

We calculate the energy spectrum of a confining flux tube that is closed around a spatial torus, as a function of its length l. We do so for various SU(N) gauge theories in 3+1 dimensions, and for various values of spin, parity and longitudinal momentum. We are able to present usefully accurate results for about 20 of the lightest such states, for a range of l that begins close to the (finite volume) deconfining phase transition, and extends up to l.sqrt(K)~6 (where K is the string tension). We find that most of these low-lying states are well described by the spectrum of the Nambu-Goto free string theory in flat space-time. Remarkably, this is so not only at the larger values of l, where the gap between the ground state energy and the low-lying excitations becomes small compared to the mass gap, but also down to much shorter lengths where these excitation energies become large compared to sqrt(K), the flux-tube no longer `looks' anything like a thin string, and an expansion of the effective string action in powers of 1/l no longer converges. All this is for flux in the fundamental representation. We also calculate the k=2 (anti)symmetric ground states and these show larger corrections at small l. So far all this closely resembles our earlier findings in 2+1 dimensions. However, and in contrast to the situation in D=2+1, we also find that there are some states, with J,P=0,- quantum numbers, that show large deviations from the Nambu-Goto spectrum. We investigate the possibility that (some of) these states may encode the massive modes associated with the internal structure of the flux tube, and we discuss how the precocious free string behaviour of most states constrains the effective string action, on which much interesting theoretical progress has recently been made.

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摘要：

英文摘要：

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