  A particularly rich class of integrable systems arises from the AdS/CFT
duality. There, the two-dimensional quantum field theory living on the string
worldsheet may be understood in terms of a non-relativistic factorized S
matrix, and the energy spectrum may be derived by techniques such as the mirror
thermodynamic Bethe ansatz or the quantum spectral curve. In the case of
AdS$_3$/CFT$_2$ without Ramond-Ramond fluxes, the worldhseet theory is a
Wess-Zumino-Witten model with continous and discrete representations which, for
the lowest allowed level, is dual to the symmetric product orbifold of a free
theory. I will show how continuous representations may arise from
integrability, and that at lowest level the Bethe equations yield the symmetric
product orbifold partition function on the nose.
