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

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.