Summing over Geometries in String Theory

Understand

We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions.

• We discuss this problem with the help of the tensionless string on $\mathcal{M}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$ (with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold $\text{Sym}^N(\mathbb{T}^4)$.
• We strengthen the analysis of arXiv:2008.07533 and show that the perturbative string partition function around a fixed bulk background already includes a sum over semi-classical geometries and large stringy corrections can be interpreted as various semi-classical geometries.
• We argue in particular that the string partition function on a Euclidean wormhole geometry factorizes completely into factors associated to the two boundaries of spacetime.