论文标题
在Narain Moduli空间上平均
Averaging Over Narain Moduli Space
论文作者
论文摘要
涉及JT重力二维的最新发展表明，在某些条件下，在边界理论的集合中，重力路径积分是双重的，而不是特定边界理论。例如，在一个维度上进行一个示例，人们想将二维CFT的随机合奏与三维的爱因斯坦重力进行比较。但这很困难。对于一个简单的问题，在这里，我们平均比Narain的二维CFT家族通过环形紧凑型获得。据信这些理论是最通用的理论，其中央电荷和Abelian当前代数对称性，因此对它们进行平均意味着与这些属性一起选择随机的CFT。可以使用数字理论的siegel-weil公式来计算平均值，并具有一些属性，暗示了散装双重理论，这将是三个维度中的外来重力理论。批量的双重理论更像是$ u（1）^{2d} $ Chern-Simons理论，而不是像爱因斯坦重力一样。
Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT's to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain's family of two-dimensional CFT's obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like $U(1)^{2D}$ Chern-Simons theory than like Einstein gravity.
