Averaging over Narain moduli space
Averaging over Narain moduli space
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DOI：
10.1007/jhep10(2020)187
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发表时间：
2020-06
影响因子：
5.4
通讯作者：
A. Maloney;E. Witten
中科院分区：
文献类型：
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作者：
A. Maloney;E. Witten
二维 JT 引力的最新进展表明，在某些条件下，引力路径积分与边界理论集合的平均值对偶，而不是与特定边界理论对偶。再举一个一维的例子，我们想将二维 CFT 的随机系综与三维的爱因斯坦引力进行比较。但这很难。对于更简单的问题，这里我们对通过环形压缩获得的 Narain 二维 CFT 系列进行平均。这些理论被认为是最通用的理论，具有中心电荷和阿贝尔电流代数对称性，因此对它们进行平均意味着选择具有这些属性的随机 CFT。平均值可以使用数论的西格尔-韦尔公式计算，并且具有一些暗示体对偶理论的性质，这将是三维重力的奇异理论。体对偶理论更像 U (1) 2D Chern-Simons 理论，而不是爱因斯坦引力。
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.