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arXiv 1406.4892hep-thhep-phnucl-th
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高表示夸克的大Nc规范理论

Large Nc gauge theory with quarks in high representations

Thomas D. Cohen, Srimoyee Sen

备注：
9 pages, 2 figures
发表信息：
Phys. Rev. D 90, 085008 (2014)
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摘要：

本文探讨了紫外完备量子场论的一个新的易处理的领域--非阿贝尔规范理论的大Nc极限，其中夸克是高维表示的（Nc的标度比Nc ^2快），例如夸克的基本指数a大于或等于3。当Nc趋于无穷大时，如果g^2 Nc^（a-1）保持不变，而不是标准的t Hooft耦合g^2 Nc，则可以得到光滑且非平凡的Nc极限，其中g是规范耦合。3+1维的SU（Nc）规范理论在大Nc时不是渐近自由的，因为它们包含的夸克的表示的尺度比Nc ^[2]快，因此不是紫外完备的。然而，在较低的时空维（2+1，1+1）中，对于任何Nc，这种理论的重整化群流总是在g = 0处有一个稳定的紫外不动点，因此该理论是紫外完备的。对于无质量夸克的情况，该理论有一个红外固定点。对于大质量夸克，理论是有局限性的。限制尺度的参数化数量级为Nc^（（2-a）/（4-d）），对于a > 2且d < 4的理论，在大Nc时被驱动到零，其中d是时空维度。

英文摘要：

This paper explores a novel tractable regime for ultraviolet-complete quantum field theories -- the large Nc limit of non-abelian gauge theories with quarks in high dimensional representations (scaling with Nc faster than Nc^2 ), such as quarks with 'a' fundamental indices with a greater than or equal to 3. A smooth and nontrivial Nc limit can be obtained if g^2 Nc^(a-1) is held fixed instead of the standard t Hooft coupling g^2 Nc as Nc goes to infinity where g is the gauge coupling. SU(Nc) gauge theories in 3+1 dimensions are not asymptotically free at large Nc when they contain quarks in representations whose dimensions scale faster than Nc^2 and hence are not ultraviolet complete. However, in lower space-time dimensions (2+1, 1+1), for any Nc, renormalization group flow for such theories always has a stable ultraviolet fixed point at g = 0; the theory is thus ultraviolet complete. For the case of massless quarks, the theory has an infrared fixed point. For massive quarks, the theory is confining. The confining scale is parametrically of the order Nc^((2-a)/(4-d)) and is driven to zero at large Nc for theories with a > 2 and d < 4 where d is the space time dimension.

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