论文标题
$ \ Mathbb {r} \ times s^1 $ in $ 1/n $扩展
Vacuum energy of the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion
论文作者
论文摘要
通过采用$ 1/n $扩展，我们计算了二维超对称（SUSY）$ \ MATHBB {C} p^{n-1} $模型的真空能量〜$ e（δε）$（Δε）$参数〜$δε$。最近，Fujimori et \ al。\使用基于Bion的半古典近似进行了大力研究，这是由红外肾上腺龙的可能的半古典图片进行的。在我们的计算中，我们发现参数〜$δε$接受重新归一化，并且在这种重新归一化后，真空能成为紫外线有限。对于$ 1/n $扩展的临近领先顺序，我们发现，通过〜$ s^1 $，$ r $，$ re（Δε）$的半径标准化的真空能量作为〜$λr$ for〜 $λr$ small的反向功率，而$λ$是动态量表。由于$λ$与重新归一化的't〜 hooft耦合〜$λ_r$ as〜$λ\ sim e^{ - 2π/2π/λ_r} $，我们可以使用$ 1/n $扩展的订单，因此真空能量纯粹是非易位的定量，并且没有明确的coupling $ $ $ $ $ $ $ $ $
By employing the $1/N$ expansion, we compute the vacuum energy~$E(δε)$ of the two-dimensional supersymmetric (SUSY) $\mathbb{C}P^{N-1}$ model on~$\mathbb{R}\times S^1$ with $\mathbb{Z}_N$ twisted boundary conditions to the second order in a SUSY-breaking parameter~$δε$. This quantity was vigorously studied recently by Fujimori et\ al.\ using a semi-classical approximation based on the bion, motivated by a possible semi-classical picture on the infrared renormalon. In our calculation, we find that the parameter~$δε$ receives renormalization and, after this renormalization, the vacuum energy becomes ultraviolet finite. To the next-to-leading order of the $1/N$ expansion, we find that the vacuum energy normalized by the radius of the~$S^1$, $R$, $RE(δε)$ behaves as inverse powers of~$ΛR$ for~$ΛR$ small, where $Λ$ is the dynamical scale. Since $Λ$ is related to the renormalized 't~Hooft coupling~$λ_R$ as~$Λ\sim e^{-2π/λ_R}$, to the order of the $1/N$ expansion we work out, the vacuum energy is a purely non-perturbative quantity and has no well-defined weak coupling expansion in~$λ_R$.
