Triality in minimal model holography

Abstract

The non-linear W∞[μ] symmetry algebra underlies the duality between the WN minimal model CFTs and the hs[μ] higher spin theory on AdS3. It is shown how the structure of this symmetry algebra at the quantum level, i.e. for finite central charge, can be determined completely. The resulting algebra exhibits an exact equivalence (a ‘triality’) between three (generically) distinct values of the parameter μ. This explains, among other things, the agreement of symmetries between the WN minimal models and the bulk higher spin theory. We also study the consequences of this triality for some of the simplest W∞[μ] representations, thereby clarifying the analytic continuation between the ‘light states’ of the minimal models and conical defect solutions in the bulk. These considerations also lead us to propose that one of the two scalar fields in the bulk actually has a non-perturbative origin.