Wrapping interactions of the $\mathrm{AdS}_3\times\mathrm{S}^3\times\mathrm{T}^4$ superstring

We address the finite volume effects of the lightcone string on the $\mathrm{AdS}_3\times\mathrm{S}^3\times\mathrm{T}^4$ background equipped with Ramond-Ramond flux. For this purpose we study an analytic structure and properties of the recently obtained Y-system, which for the first time accounts for all particle sectors in $\mathrm{AdS}_3$. Specifically, we demonstrate its solvability in the generic non-BPS sector, which allows to establish the ground state energy of the $\mathrm{AdS}_3$ string from its mirror theory. We also provide an independent derivation from the generalized Lüscher formalism and find complete agreement with our results from the Thermodynamic Bethe Ansatz. In addition, several new non-perturbative properties arise from TBA in various string regimes, which we also derive for $\mathrm{AdS}_5\times\mathrm{S}^5$ and perform comparison. In the given context, we explore large tension of the $\mathrm{AdS}_3$ lightcone string with quasiperiodic fields.