论文标题
关于$ t \ bar {t} $ cft的紫外线完成的分类
On the classification of UV completions of integrable $T \bar{T}$ deformations of CFT
论文作者
论文摘要
众所周知，不相关的$ t \ bar {t} $ dimension $ 4 $扰动具有通用属性。特别是，对于最有趣的情况，该理论在超紫罗兰（UV）中发展出奇异性，表示最短的距离，并且在应用到字符串理论中的Hagedorn过渡中。我们表明，通过添加无限数量的较高$ [t \ bar {t}] _ {s> 1} $与调谐耦合无关的操作员，可以解决此奇异性，并且该理论与UV Central Chartral Charter $ c _ {\ rm uv uv} $。我们提出了一种对可能集成的紫外线完成分类的方法。对于具有$ c _ {\ rm ir} = \ tfrac {1} {2} $的ISING模型，我们根据单个无质量的Majorana fermion描述找到了3个UV完成，带有$ C _ {\ rm UV} = \ tfrac {\ tfrac {7} {7} {10} {10} {10} {10} {10} $ and $ \ tfrac = n} = 1 $ supersymmetry，以前是已知的，我们认为这些是基于这种粒子谱的分类问题的唯一解决方案。我们发现3个与Lie Group $ E_8 $相关的8个无质量粒子的频谱，适用于$ c _ {\ rm UV} = \ tfrac {21} {21} {22}，\ tfrac {15} {2} {2} {2} {2} $ and $ \ \ tfrac {21} $ \ tfrac {22} $ c _ {\ rm UV} = \ tfrac {21} {22} $我们认为，此$ E_8 $频谱可能还有更多案例。我们还基于$ {\ rm su（3）} $和$ {\ rm su（4）} $研究了更简单的情况，我们可以在其中提出完整的分类。对于$ {\ rm su（3）} $，Infra-Red（ir）理论是具有$ C _ {\ rm ir} = \ tfrac {4} {5} $的三态POTTS模型，我们找到了3个完整的，$ \ tfrac {4} {4} {4} {5} {5} {5} <c _} \ tfrac {16} {5} $。对于$ {\ rm su（4）} $ case，它具有$ 3 $颗粒和$ c _ {\ rm ir} = 1 $，我们发现$ 11 $ UV完成，$ 1 <c _ {\ rm UV} \ leq 5 $，其中大多数以前是未知的。
It is well understood that 2d conformal field theory (CFT) deformed by an irrelevant $T\bar{T}$ perturbation of dimension $4$ has universal properties. In particular, for the most interesting cases, the theory develops a singularity in the ultra-violet (UV), signifying a shortest possible distance, with a Hagedorn transition in applications to string theory. We show that by adding an infinite number of higher $[T\bar{T}]_{s>1}$ irrelevant operators with tuned couplings, this singularity can be resolved and the theory becomes UV complete with UV central charge $c_{\rm UV}$. We propose an approach to classifying the possible UV completions that are integrable. For the Ising model with $c_{\rm IR} = \tfrac{1}{2}$ we find 3 UV completions based on a single massless Majorana fermion description with $c_{\rm UV} = \tfrac{7}{10}$ and $ \tfrac{3}{2}$, which both have ${\cal N}=1$ supersymmetry and were previously known, and we argue that these are the only solutions to our classification problem based on this spectrum of particles. We find 3 additional ones with a spectrum of 8 massless particles related to the Lie group $E_8$ appropriate to a magnetic perturbation with $c_{\rm UV} = \tfrac{21}{22} , \tfrac{15}{2}$ and $\tfrac{31}{2}$. We argue that it is likely there are more cases for this $E_8$ spectrum. We also study simpler cases based on ${\rm su(3)}$ and ${\rm su(4)}$ where we can propose complete classifications. For ${\rm su(3)}$ the infra-red (IR) theory is the 3-state Potts model with $c_{\rm IR} = \tfrac{4}{5}$ and we find 3 completions with $\tfrac{4}{5} < c_{\rm UV} \leq \tfrac{16}{5}$. For the ${\rm su(4)}$ case, which has $3$ particles and $c_{\rm IR} =1$, and we find $11$ UV completions with $1 < c_{\rm UV} \leq 5$, most of which were previously unknown.
