Closed Strings and Moduli in $AdS_3/CFT_2$

TL;DR

This work investigates perturbative closed strings on AdS_3 x S^3 x T^4 across the full 20-dimensional moduli space, focusing on the H_(0,0) sector. In the D1/D5 (RR) background, four moduli modify the spectrum, with the primary effect being a shift in the AdS_3 radius R; in the F1/NS5 (NSNS) background, four moduli introduce RR couplings that render the worldsheet theory integrable via known S matrices and Bethe equations. Across both backgrounds, the worldsheet theory remains integrable for weak coupling, and the spectrum is computable through exact-in-R Bethe ansatz techniques, with the moduli entering only through the radius and coupling h(R). The results strengthen the connection between string moduli, integrability, and the AdS_3/CFT_2 correspondence, and offer a framework to compare with Sym_N orbifold and potential Higgs branch CFT interpretations. The analysis also highlights a unified treatment of TrT deformations, gauge fixing, and off-shell algebras in preserving integrability across the moduli space.

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.