Partition functions of the tensionless string

TL;DR

The paper studies tensionless strings on $ ext{AdS}_3 imes ext{S}^3 imes ext{T}^4$ with NS-NS flux 1, arguing for a dual description by $ ext{Sym}^N( ext{T}^4)$ and showing that the full boundary partition function is captured by a single bulk geometry via holomorphic covering maps. It computes the one-loop string partition function on thermal $ ext{AdS}_3$ and conical defects, demonstrates a black hole/long-string duality, and explains how the factorization puzzle is resolved by background-dependent spectrum rearrangements, with the bulk partition function effectively independent of bulk geometry beyond boundary data. The results reveal a concrete realization of the black hole/string transition and establish a grand-canonical framework that reproduces the symmetric product orbifold partition function, while highlighting localization, one-loop exactness, and potential extensions to higher-genus boundaries and wormholes. The work suggests deep connections between bulk geometry and boundary spectra in the tensionless limit and points to future directions in Euclidean wormholes, localization proofs, and Lorentzian generalizations, with implications for AdS$_3$/CFT$_2$ and higher-spin symmetry structures.

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.