格点规范理论中能量-动量张量关联函数的截止效应
Cutoff Effects on Energy-Momentum Tensor Correlators in Lattice Gauge Theory
摘要：
研究了在有限温度下，在Wilson作用量和$T_{μν}$的两种不同离散下，SU（$N_c$）规范理论中能量动量张量$T_{μν}$的离散误差对量子数的影响.我们这样做是通过使用晶格微扰理论和非微扰蒙特卡罗模拟。这些关联函数是欧几里得时间$x_0$和空间动量${\bf p}$的函数，是研究胶子等离子体输运性质的晶格出发点。我们发现能量相关器$\int d^3x T_{00}$比动量相关器$\int d^3x T_{0k}$有更大的离散化误差。其次，剪切和对角应力关联函数（$T_{12}$和$T_{kk}$）要求$\Nt\geq 8$使$Tx_0={1/2}$点处于标度区域，并且截止效应小于10%。然后，我们表明，他们的离散误差的各向异性晶格与$\as/\at=2$是可比的各向同性晶格上具有相同的时间晶格间距。最后，我们还研究了有限${\bf p}$关联函数。
英文摘要：
We investigate the discretization errors affecting correlators of the energy-momentum tensor $T_{μν}$ at finite temperature in SU($N_c$) gauge theory with the Wilson action and two different discretizations of $T_{μν}$. We do so by using lattice perturbation theory and non-perturbative Monte-Carlo simulations. These correlators, which are functions of Euclidean time $x_0$ and spatial momentum ${\bf p}$, are the starting point for a lattice study of the transport properties of the gluon plasma. We find that the correlator of the energy $\int d^3x T_{00}$ has much larger discretization errors than the correlator of momentum $\int d^3x T_{0k}$. Secondly, the shear and diagonal stress correlators ($T_{12}$ and $T_{kk}$) require $\Nt\geq 8$ for the $Tx_0={1/2}$ point to be in the scaling region and the cutoff effect to be less than 10%. We then show that their discretization errors on an anisotropic lattice with $\as/\at=2$ are comparable to those on the isotropic lattice with the same temporal lattice spacing. Finally, we also study finite ${\bf p}$ correlators.
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