arXiv 2007.038802020-07hep-thcond-mat.str-elhep-lat

通过TQFT耦合的强耦合QFT动力学

Strongly coupled QFT dynamics via TQFT coupling

Mithat Ünsal

备注：: 90 pages, 8 figures, Minor changes, Refs. added
DOI：: 10.1007/JHEP11(2021)134

摘要：

我们考虑一类量子场论和量子力学，我们耦合到$\mathbb Z_N$拓扑QFT，为了分类的非微扰效应在原来的理论。$\mathbb Z_N$ TQFT结构自然产生于打开$\mathbb Z_N$ 0-或1-形式全局对称的经典背景场。在$\mathbb Z_N$ Yang-Mills理论中，非微扰展开参数在半经典弱耦合域和强耦合域均为$\exp[-S_I/N]= \exp[-{8 π^2}/{g^2N}]$，对应于分数拓扑电荷组态.为了对原始$SU(N)$理论中的非微扰效应进行分类，我们必须使用$PSU(N)$束流和升力构型（无穷远处的临界点），对于这些构型，回到$SU(N)$是没有障碍的。这些提供了一个完善的瞬子和：整数拓扑电荷，但至关重要的分数行动配置的贡献，提供了一个TQFT保护的复苏半经典扩展到强耦合的推广。$T^3 \times S^1_L$上的单极瞬子（或分数瞬子）可以解释为$PSU(N)$束中的“t Hooft通量背景中的隧穿事件。该结构为研究QFT的强耦合机制提供了一个新的视角，并解决了一些老问题，特别是解决了大$N$和瞬子分析之间的矛盾。我们导出了$\mathbb{CP}^{1}$模型中$θ=0$处的质量间隙和$θ=π$处的无间隙，以及$\mathbb R^2$上$\mathbb{CP}^{N-1}, N \geq 3$中任意$θ$处的质量间隙.

英文摘要：

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 $\mathbb R^2$.

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英文摘要：

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