Closed Strings and Moduli in $AdS_3/CFT_2$

TL;DR

This paper studies how the spectrum of closed strings in $AdS_3 imes S^3 imes T^4$ varies with moduli, revealing that only a few moduli influence energies at weak coupling and that integrability persists across the moduli space.

Contribution

It demonstrates that the worldsheet theory remains integrable throughout the entire 20-dimensional moduli space, with specific effects of moduli in RR and NSNS backgrounds.

Findings

Only four moduli affect energies at weak coupling.

In RR background, moduli change the curvature radius.

In NSNS background, moduli introduce worldsheet interactions enabling integrability.

Abstract

String theory on $AdS_3 \times S^3 \times T^4$ has 20 moduli. We investigate how the perturbative closed string spectrum changes as we move around this moduli space in both the RR and NSNS flux backgrounds. We find that, at weak string coupling, only four of the moduli affect the energies. In the RR background the only effect of these moduli is to change the radius of curvature of the background. On the other hand, in the NSNS background, the moduli introduce worldsheet interactions which enable the use of integrability methods to solve the spectral problem. Our results show that the worldsheet theory is integrable across the 20 dimensional moduli space.