Holomorphic structure of massive scalar fields in (A)dS2

A bstract Scalar field theories in (A)dS 2 with integer scaling dimensions ∆ = k + 1 are characterised 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, taking care to treat AdS 2 and dS 2 separately. In particular, we point out that the theories admit mode expansions reminiscent of standard two-dimensional conformal field theories in complex coordinates, with which we are able to construct a large set of symmetry transformations which includes Virasoro symmetry. We further leverage holomorphicity of the currents to show that the significant subset of the full symmetries of theories with k > 0 is captured by a chiral algebra, which is a subalgebra of the one in the k = 0 (massless) theory. This allows us to identify integrable deformations for k ∈ {0 , 1 , 2}. We finally observe that a lack of integrable deformations for k > 2 is a consequence of a known conjecture.