论文标题
（2+1）d $ ϕ^4 $ - 来自哈密顿截断的理论的非扰动动力
Nonperturbative dynamics of (2+1)d $ϕ^4$-theory from Hamiltonian truncation
论文作者
论文摘要
我们使用LightCone Condomal截断（LCT）（Hamiltonian截断的一种版本）来研究2+1个维度中$ ϕ^4 $ - 理论的非扰动，实时动力学。该理论具有需要调节的紫外线差异。我们回顾一下，在具有总能量截止的哈密顿框架中，重新归一定化必然是\ emph {state依赖性}，并且不能用标准的本地操作员对抗来取消紫外线灵敏度。为了克服这个问题，我们提出了用于构建（2+1）d $ ϕ^4 $的适当状态依赖性对抗的处方。然后，我们将LCT与此反式处方一起研究$ ϕ^4 $ - 理论，重点关注$ \ Mathbb {z} _2 $ symmetry-symetry-symetry-wearserving阶段。具体而言，我们计算频谱是耦合的函数，并在（方案依赖性）临界耦合下演示了质量间隙的闭合。我们还计算了Lorentz-Invariant的两点函数，无论是在通用的强耦合和临界点附近，我们都证明了IR普遍性和消失应力张量的痕迹。
We use Lightcone Conformal Truncation (LCT) -- a version of Hamiltonian truncation -- to study the nonperturbative, real-time dynamics of $ϕ^4$-theory in 2+1 dimensions. This theory has UV divergences that need to be regulated. We review how, in a Hamiltonian framework with a total energy cutoff, renormalization is necessarily \emph{state-dependent}, and UV sensitivity cannot be canceled with standard local operator counterterms. To overcome this problem, we present a prescription for constructing the appropriate state-dependent counterterms for (2+1)d $ϕ^4$-theory in lightcone quantization. We then use LCT with this counterterm prescription to study $ϕ^4$-theory, focusing on the $\mathbb{Z}_2$ symmetry-preserving phase. Specifically, we compute the spectrum as a function of the coupling and demonstrate the closing of the mass gap at a (scheme-dependent) critical coupling. We also compute Lorentz-invariant two-point functions, both at generic strong coupling and near the critical point, where we demonstrate IR universality and the vanishing of the trace of the stress tensor.
