剪切通道的格点规范理论求和定则
Lattice Gauge Theory Sum Rule for the Shear Channel
摘要：
本文导出了SU（$N_c$）格点规范理论中剪应力的$(ω,p)=0$热关联的精确表达式。我采取适当的线性组合的剪切相关器和相关的能量密度，消除对数发散。算子乘积展开式表明，当$ω\to\infty$ .由此可见，真空减去剪切谱函数消失在大频率至少一样快的$α_s^2(ω)$，并遵守求和规则。迹线异常对谱求和规则有潜在的贡献，这一贡献仍有待充分计算，但我估计对于$T\gtrsim 3T_c$来说，这一贡献在数值上很小。与体通道相比，剪切通道的谱密度与真空中的谱密度相比整体增强。
英文摘要：
An exact expression is derived for the $(ω,p)=0$ thermal correlator of shear stress in SU($N_c$) lattice gauge theory. I remove a logarithmic divergence by taking a suitable linear combination of the shear correlator and the correlator of the energy density. The operator product expansion shows that the same linear combination has a finite limit when $ω\to\infty$. It follows that the vacuum-subtracted shear spectral function vanishes at large frequencies at least as fast as $α_s^2(ω)$ and obeys a sum rule. The trace anomaly makes a potential contribution to the spectral sum rule which remains to be fully calculated, but which I estimate to be numerically small for $T\gtrsim 3T_c$. By contrast with the bulk channel, the shear channel spectral density is then overall enhanced as compared to the spectral density in vacuo.
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