Partition functions of the tensionless string

TL;DR

This paper computes the partition functions of tensionless strings on various AdS3 backgrounds, showing independence from bulk geometry and providing insights into string-black hole duality and the factorization problem.

Contribution

It demonstrates that the tensionless string partition function depends only on boundary geometry, not bulk details, and establishes a concrete example of string-black hole duality.

Findings

Partition function is geometry-independent, depending only on boundary.

Thermal AdS3 and BTZ black hole are dual descriptions.

Supports a resolution to the factorization problem in holography.

Abstract

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.