Description
It is well-known that conformal transformations and closely related to holomorphicity in two dimensions. In particular, holomorphic operators such as the stress tensor in a conformal field theory can be used to show holomorphic splitting of the classical phase space of solutions. In this talk, I will argue this is also a feature of certain massive scalar fields in (A)dS_2 with integer scaling dimensions \Delta = k+1, marked by the existence of a pair of (anti-)holomorphic higher-spin currents. We explore the consequences of this to describe their quantisation and subsets of their linear and non-linear symmetries. In particular, we point out that the theories admit mode expansions reminiscent of standard 2d CFTs in complex coordinates, with which we are able to construct operators implementing global conformal transformations and Virasoro symmetry. We further leverage holomorphicity of the currents to show that the full set of symmetries of theories with k>0 is captured by a chiral algebra, contained in the one of the massless theory. This allows us to identify integrable deformations for k \leq 2.