# Partition functions of the tensionless string

Research paper by **Lorenz Eberhardt**

Indexed on: **19 Aug '20**Published on: **17 Aug '20**Published in: **arXiv - High Energy Physics - Theory**

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#### 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.