论文标题
张力无拉的弦的分区功能
Partition functions of the tensionless string
论文作者
论文摘要
我们在$ \ text {ads} _3 \ times \ text {s}^3 \ times \ mathbb {t}^4 $中，在$ \ text {ads} _3 \ times \ times \ times \ text {s}^4 $中考虑字符串理论，并带有NS-NS Flux的一个单位。该理论是为了描述对称产品Orbifold CFT的猜测。我们考虑在不同的欧几里得背景上的字符串，例如热$ \ text {ads} _3 $，BTZ黑洞，锥形缺陷和虫洞几何形状。在简单的示例中，我们计算完整的字符串分区功能。我们发现它与精确的散装几何形状无关，但仅取决于保形边界的几何形状。例如，在热$ \ text {ads} _3 $上的字符串分区函数显示，带有圆环边界的锥形缺陷被证明是一致的，因此为这些不同的背景几何形状上的无张力弦的等效性提供了证据。我们还发现，热$ \ text {ads} _3 $，而BTZ黑洞是双描述，BTZ黑洞的真空映射到单个长字符串绕线绕线绕过热$ \ text {ads} _3 $。因此，系统产生了弦黑孔跃迁的具体示例。因此，重现边界分区函数不需要大量几何形状的总和，而是在具有适当边界的任何散装几何形状上与字符串分区函数一致。我们认为，当考虑具有断开界限的几何形状时，相同的机制可以导致分解问题的解决，因为连接和断开的几何形状给出了相同的贡献，并且我们不必单独包括它们。
We consider string theory on $\text{AdS}_3 \times \text{S}^3 \times \mathbb{T}^4$ in the tensionless limit, with one unit of NS-NS flux. This theory is conjectured to describe the symmetric product orbifold CFT. We consider the string on different Euclidean backgrounds such as thermal $\text{AdS}_3$, the BTZ black hole, conical defects and wormhole geometries. In simple examples we compute the full string partition function. We find it to be independent of the precise bulk geometry, but only dependent on the geometry of the conformal boundary. For example, the string partition function on thermal $\text{AdS}_3$ and the conical defect with a torus boundary is shown to agree, thus giving evidence for the equivalence of the tensionless string on these different background geometries. We also find that thermal $\text{AdS}_3$ and the BTZ black hole are dual descriptions and the vacuum of the BTZ black hole is mapped to a single long string winding many times asymptotically around thermal $\text{AdS}_3$. Thus the system yields a concrete example of the string-black hole transition. Consequently, reproducing the boundary partition function does not require a sum over bulk geometries, but rather agrees with the string partition function on any bulk geometry with the appropriate boundary. We argue that the same mechanism can lead to a resolution of the factorization problem when geometries with disconnected boundaries are considered, since the connected and disconnected geometries give the same contribution and we do not have to include them separately.
