论文标题
平均代码和$ su（2）$模块化bootstrap
Averaging over codes and an $SU(2)$ modular bootstrap
论文作者
论文摘要
已知错误校正的代码可以定义手性2D晶格CFT，其中所有$ u（1）$ symmetries都将增强到$ su（2）$。在本文中，我们将此构造扩展到更广泛的长度 - $ n $代码，这些代码定义了使用$ su（2）^n $对称的完整（非手续）CFT，其中$ n = c+\ bar c $。我们表明，代码提供了自然离散的2D理论集合，其中可以计算平均可观察物。发现从所有代码上平均加权获得的分区函数被发现由总和的模块化图像在整个扩展对称组的真空特征的模块化图像上给出，在这种情况下，模块化图像的数量是有限的。该平均分区功能具有较大的差距，在整个$ su（2）^n $对称组的初选中用$ n $线性缩放。使用模块化图像上的总和，我们猜想了属-2分区函数的形式。这表现出对巨额双重虫洞解的断开边界特征的连接贡献。
Error-correcting codes are known to define chiral 2d lattice CFTs where all the $U(1)$ symmetries are enhanced to $SU(2)$. In this paper, we extend this construction to a broader class of length-$n$ codes which define full (non-chiral) CFTs with $SU(2)^n$ symmetry, where $n=c+\bar c$. We show that codes give a natural discrete ensemble of 2d theories in which one can compute averaged observables. The partition functions obtained from averaging over all codes weighted equally is found to be given by the sum over modular images of the vacuum character of the full extended symmetry group, and in this case the number of modular images is finite. This averaged partition function has a large gap, scaling linearly with $n$, in primaries of the full $SU(2)^n$ symmetry group. Using the sum over modular images, we conjecture the form of the genus-2 partition function. This exhibits the connected contributions to disconnected boundaries characteristic of wormhole solutions in a bulk dual.
