论文标题
通过TQFT耦合强烈耦合QFT动力学
Strongly coupled QFT dynamics via TQFT coupling
论文作者
论文摘要
我们考虑了一类量子场理论和量子力学，我们将其与$ \ Mathbb z_n $拓扑QFTS相结合，以便在原始理论中对非扰动效应进行分类。 $ \ mathbb z_n $ tqft结构自然而然地来自于$ \ mathbb z_n $ 0-或1形式全局对称性的经典背景字段。在$ su（n）$ yang-mills理论与$ \ mathbb z_n $ tqft结合在一起，非扰动扩展参数为$ \ exp [-s_i/n] = \ exp [ - {8π^2}/{g^2}/{g^2n}配置。为了对原始$ su（n）$理论中的非扰动效果进行分类，我们必须使用$ psu（n）$捆绑包和提升配置（无限临界点），没有障碍物回到$ su（n）$。这些提供了Instanton总和的完善：整数拓扑电荷，但至关重要的分数作用构型有助于促进TQFT的保护，可保护复杂的半经典扩展对强耦合的概括。 $ t^3 \ times s^1_l $上的monopole-instantons（或分数instantons）可以解释为$ psu（n）$ bundle中的hooft通量背景中的隧道事件。该构建为QFTS强大的耦合制度提供了新的视角，并解决了许多旧的常规问题，尤其是解决了大型$ n $和Instanton分析之间的冲突。我们将质量差距定为$θ= 0 $，而无差距为$θ=π$，in $ \ mathbb {cp}^{1} $型号，以及$ \ mathbb {cp}^cp}^{n-1}^{n-1}，n \ geq 3 $ on $ for $ \ geq 3 $ on $ \ mathbb r r^2 $ in nutumary $θ$的质量差距。
We consider a class of quantum field theories and quantum mechanics, which we couple to $\mathbb Z_N$ topological QFTs, in order to classify non-perturbative effects in the original theory. The $\mathbb Z_N$ TQFT structure arises naturally from turning on a classical background field for a $\mathbb Z_N$ 0- or 1-form global symmetry. In $SU(N)$ Yang-Mills theory coupled to $\mathbb Z_N$ TQFT, the non-perturbative expansion parameter is $\exp[-S_I/N]= \exp[-{8 π^2}/{g^2N}]$ both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original $SU(N)$ theory, we must use $PSU(N)$ bundle and lift configurations (critical points at infinity) for which there is no obstruction back to $SU(N)$. These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on $T^3 \times S^1_L$ can be interpreted as tunneling events in the 't Hooft flux background in the $PSU(N)$ bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-$N$ and instanton analysis. We derive the mass gap at $θ=0$ and gaplessness at $θ=π$ in $\mathbb{CP}^{1}$ model, and mass gap for arbitrary $θ$ in $\mathbb{CP}^{N-1}, N \geq 3$ on $\mathbb R^2$.
