Recent developments in the AdS3/CFT2 correspondence with mixed flux

In this talk, I will present our last results regarding the classical integrable structure of the AdS₃/CFT₂ correspondence with mixed three-form fluxes. The first result involves the study of the one-loop correction of spinning strings. We have analysed how the quadratic fluctuations around the simplest solution in this family depend on the mixing parameter. In particular, we found that the one-loop correction vanishes in the pure NS-NS flux limit. The second result is based on the analysis of minimal surfaces in this background. We have found classical solutions ending in two concentric circumferences and their spectral curve. It turns out that the NS-NS flux either brings the surface near to the boundary or separates the circumferences, whereas it contracts one of the cycles of the spectral curve. The third result concerns the semi-classical spin chain representation associated to the pure NS-NS flux limit of the setting. We have shown that the Landau-Lifshitz limit of the spin chain agrees with in the semi-classical results, although the computation bears some differences with the usual one.