论文标题
Ricci平坦的漫长路
Long Way to Ricci Flatness
论文作者
论文摘要
我们研究二维加权$ {\ Mathcal n} = 2 $ supersymmetric $ \ mathbb {cp} $模型，目的是探索其红外（IR）限制。 $ \ mathbb {wcp}（n，\ widetilde {n}）$是在四维$ {\ mathcal n} = 2 $ qcd中简化的非阿布莱恩字符串的世界表理论版本。在衡量的线性Sigma模型（GLSM）公式中，$ \ Mathbb {wcp}（n，\ wideTilde {n}）$具有$ n $费用+1和$ \ widetilde {n} $费用费用$ -1 $ -1 $ -1 $ fields。众所周知，在$ \ wideTilde {n} = n $的情况下，此glsm是共形的。据信它的目标空间是非紧密的卡拉比远流动。我们主要专注于$ n = 2 $ case，然后卡拉比（Calabi-Yau）空间是一个Conifold。 另一方面，在非线性Sigma模型（NLSM）中，该模型具有超紫罗莱对数，并且看起来不一致。此外，它的度量不是ricci-flat。我们通过研究模型的重新归一化组（RG）流来解决这个难题。我们表明，NLSM的度量成为IR中的ricci-flat。此外，它倾向于已知的已解决的conifold指标。我们还研究了$ \ Mathbb {WCP} $模型的近亲 - 所谓的$ Zn $模型 - 实际上，该模型代表了非亚伯来语半op of的世界表理论，并表明该$ Zn $模型具有相似的RG属性。
We study two-dimensional weighted ${\mathcal N}=2$ supersymmetric $\mathbb{CP}$ models with the goal of exploring their infrared (IR) limit. $\mathbb{WCP}(N,\widetilde{N})$ are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional ${\mathcal N}=2$ QCD. In the gauged linear sigma model (GLSM) formulation, $\mathbb{WCP} (N,\widetilde{N})$ has $N$ charges +1 and $\widetilde{N}$ charges $-1$ fields. As well-known, at $\widetilde{N}=N$ this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the $N=2$ case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the $\mathbb{WCP}$ model -- the so called $zn$ model -- which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this $zn$ model has similar RG properties.
