Lukas Lindwasser

Title: Holomorphicity versus conformal symmetry in (A)dS_2

 

Abstract: In two dimensions, holomorphicity and conformal symmetry are deeply connected, with conformal symmetry implying holomorphicity, and the converse also often true. In this talk, I will discuss a set of theories that illustrate the subtlety of this connection. On constant curvature surfaces like (A)dS_2, there exists a sequence of non-conformally coupled massive fields labelled by an integer k>0 that admit holomorphic, rank k+1 conserved currents. Although their standard stress tensor is not traceless, a sub-sector of correlation functions obeys global conformal Ward identities, indicating a hidden conformal invariance. I will reveal that this conformal symmetry manifests as a non-local action on the fields. Moreover, I will show that the symmetry action localizes in an equivalent description of these theories in terms of conformal Killing tensors. In this description, the holomorphicity and conformal symmetry are thereby given a common geometric origin. Other consequences of the holomorphicity of these massive fields are discussed.