论文标题
平均自由CFT的引力双重二元格在Narain晶格上
Gravitational dual of averaged free CFT's over the Narain lattice
论文作者
论文摘要
最近有人认为，可以通过$ u \ left的Chern-Simons理论（1 \ right）^{d} \ times u \ left（1 \ oyt）^{d} $的Chern-simons理论在Narain晶格上的平均值来描述，并确切的处方是三二维式携带式托管。我们表明，Einstein Grattity将在AD $ _ {3} $上提供这些平均CFT的引力双重，并提供$ u \ left（1 \ right）^{d-1} \ times u \ left（1 \ weles（1 \ oright）^{d-1} $ gauge fields，与精确的条件紧密相关的是柔和的ro.然后，引力激发沿对角线$ sl \ left（2，\ mathbb {r} \右）$发电机，以便由$ u \ u \ left（1 \ right）^{d} \ times times u \ weft（1 \ weft（1 \ right（1 \ right）^d} $ courtents跨越渐近对称性。然后，通过扭曲的Sugawara结构，可以将应力 - 能量张量视为这些电流的复合物。我们的边界条件使得对于减少的相空间，在重力和纯粹的阿贝尔理论中的配置之间存在一对一的图。然后，也可以从非阿布尔的Chern-Simons理论中执行批量的分区功能，以$ sl \ left（2，\ mathbb {r} \ right）\ times u \ weft（1 \ right）^{d-1} $生成器，或通过沿允许的元件组成的途径正式组成。新的边界条件自然可容纳BTZ黑洞，然后微观的状态数量显然是正面的，并且是从散装中的分区函数中适当说明的。还简要解决了通过较高自旋重力的延伸扭曲的sugawara结构的较高自旋电流。
It has been recently argued that the averaging of free CFT's over the Narain lattice can be holographically described through a Chern-Simons theory for $U\left(1\right)^{D}\times U\left(1\right)^{D}$ with a precise prescription to sum over three-dimensional handlebodies. We show that a gravitational dual of these averaged CFT's would be provided by Einstein gravity on AdS$_{3}$ with $U\left(1\right)^{D-1}\times U\left(1\right)^{D-1}$ gauge fields, endowed with a precise set of boundary conditions closely related to the "soft hairy" ones. Gravitational excitations then go along diagonal $SL\left(2,\mathbb{R}\right)$ generators, so that the asymptotic symmetries are spanned by $U\left(1\right)^{D}\times U\left(1\right)^{D}$ currents. The stress-energy tensor can then be geometrically seen as composite of these currents through a twisted Sugawara construction. Our boundary conditions are such that for the reduced phase space, there is a one-to-one map between the configurations in the gravitational and the purely abelian theories. The partition function in the bulk could then also be performed either from a non-abelian Chern-Simons theory for two copies of $SL\left(2,\mathbb{R}\right)\times U\left(1\right)^{D-1}$ generators, or formally through a path integral along the family of allowed configurations for the metric. The new boundary conditions naturally accommodate BTZ black holes, and the microscopic number of states then appears to be manifestly positive and suitably accounted for from the partition function in the bulk. The inclusion of higher spin currents through an extended twisted Sugawara construction in the context of higher spin gravity is also briefly addressed.
