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arXiv 1709.09264hep-lathep-phhep-th
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多味规范理论的线性西格玛模型

A linear sigma model for multiflavor gauge theories

Y. Meurice

备注：
6 pages, 2 figures, uses revtex, references added
发表信息：
Phys. Rev. D 96, 114507 (2017)
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摘要：

我们考虑描述$2N_f^2$玻色子（$σ$，${\bf a_0}$，$η'$和${\bf π}$）的线性西格玛模型作为$N_f$狄拉克费米子在基本表象中的$SU(3)$定域规范理论的近似有效理论.该模型有一个可重正化的$U(N_f)_L\bigotimes U(N_f)_R$不变部分，它有一个近似的$O(2N_f^2)$对称性，和两个额外的条款，一个描述的影响，一个$SU(N_f)_V$不变质量项和其他的影响的轴异常。我们计算了任意$N_f$的光谱。利用LatKMI合作的初步和已发表的晶格结果，我们发现了随显式手性对称性破缺和$N_f$缓慢变化的质量组合。这表明异常项在质谱中起主导作用，并且简单公式（如$M_σ^2\simeq (2/N_f-C_σ)M_{η'}^2$）应适用于手性限度。$M_{η'}^2$和近似常数如$C_σ$的晶格测量可以帮助定位共形窗口的边界。我们表明，我们的计算可以适用于任意表示的规范组，特别是最小的模型与两个sextets，类似的模式可能适用。

英文摘要：

We consider a linear sigma model describing $2N_f^2$ bosons ($σ$, ${\bf a_0}$, $η'$ and ${\bf π}$) as an approximate effective theory for a $SU(3)$ local gauge theory with $N_f$ Dirac fermions in the fundamental representation. The model has a renormalizable $U(N_f)_L\bigotimes U(N_f)_R$ invariant part, which has an approximate $O(2N_f^2)$ symmetry, and two additional terms, one describing the effects of a $SU(N_f)_V$ invariant mass term and the other the effects of the axial anomaly. We calculate the spectrum for arbitrary $N_f$. Using preliminary and published lattice results from the LatKMI collaboration, we found combinations of the masses that vary slowly with the explicit chiral symmetry breaking and $N_f$. This suggests that the anomaly term plays a leading role in the mass spectrum and that simple formulas such as $M_σ^2\simeq (2/N_f-C_σ)M_{η'}^2$ should apply in the chiral limit. Lattice measurements of $M_{η'}^2$ and of approximate constants such as $C_σ$ could help locating the boundary of the conformal window. We show that our calculation can be adapted for arbitrary representations of the gauge group and in particular to the minimal model with two sextets, where similar patterns are likely to apply.

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