Strings and near-extremal black holes in theories with large $\mathcal{N}=4$ superconformal symmetry

TL;DR

This paper analyzes the superstring partition function in an AdS3 background with large 4 supersymmetry, connecting boundary currents, black hole spectra, and string theory limits, revealing new insights into near-extremal black holes and worldsheet CFTs.

Contribution

It demonstrates how the superstring spectrum encodes boundary currents and black hole excitations in theories with large 4 supersymmetry, and explores the string theory limit at the string scale.

Findings

Supergravity spectrum is recovered from the partition function.

Boundary currents are encoded in the string spectrum.

The BPS index captures excitations around supersymmetric BTZ black holes.

Abstract

We study the one-loop partition function of superstrings in the $\mathrm{AdS}_3 \times \mathbf{S}^3 \times \mathbf{S}^3 \times \mathbf{S}^1$ background. Specifically, we show that the supergravity spectrum, which contains non-chiral primary states unlike other similar $\mathrm{AdS}_3$ backgrounds, can be recovered by this partition function in the semiclassical limit. We also show how the boundary currents are encoded in the string spectrum. Furthermore, we discuss the effect of these boundary currents in the quantum partition function of near-extremal black holes in theories with large $\mathcal{N} = (4,4)$ supersymmetry, recovering results consistent with the analysis of the near-horizon (super-)Schwarzian theory. In particular, we show how the BPS index of the large $\mathcal{N} = (4,4)$ theory, which turns out to be temperature dependent, captures the spectrum of excitations around supersymmetric BTZ black holes. Finally, we comment on the limit when the AdS curvature radius is string scale, which is directly accessible within the RNS formalism for this compactification. The spectrum of the limiting theory we obtain differs from the tensionless string spectrum derived in the literature, suggesting that there is not a unique worldsheet CFT for this value of parameters.