论文标题
非独立CFT的稳定性分析
Stability Analysis of a Non-Unitary CFT
论文作者
论文摘要
我们研究了最低维操作员的不稳定性（\ it，即\ rm \ rm其操作员尺寸的假想部分）在等级$ q $ traceless的对称表示$（n）$ o（n）$ wilson-fisher固定点$ d = 4+ε$中。我们找到了一种新的半古典弹跳解决方案，该解决方案为$ o \ left的运算符（{ε^{ - 1/2}}} \ exp \ left [ - \ frac {n+8} {3εq）f（εq）\ right] \ frac {n+8} {6 \ sqrt {3}} $已修复。还计算出$ f（εq）$的形式，标准化为$ f（0）= 1 $。即使$ q $有限，这种非扰动校正仍会继续产生领先效果，这表明操作员的不稳定$ q $。我们还观察到$εq= \ frac {n+8} {6 \ sqrt {3}} $与BONCES相关的相关的相变，类似于GROSS-WITTEN-WITTEN-WADIA TRUNSITION。
We study instability of the lowest dimension operator (\it i.e., \rm the imaginary part of its operator dimension) in the rank-$Q$ traceless symmetric representation of the $O(N)$ Wilson-Fisher fixed point in $D=4+ε$. We find a new semi-classical bounce solution, which gives an imaginary part to the operator dimension of order $O\left({ε^{-1/2}}\exp\left[-\frac{N+8}{3ε}F(εQ)\right]\right)$ in the double-scaling limit where $εQ \leq \frac{N+8}{6\sqrt{3}}$ is fixed. The form of $F(εQ)$, normalised as $F(0)=1$, is also computed. This non-perturbative correction continues to give the leading effect even when $Q$ is finite, indicating the instability of operators for any values of $Q$. We also observe a phase transition at $εQ=\frac{N+8}{6\sqrt{3}}$ associated with the condensation of bounces, similar to the Gross-Witten-Wadia transition.
