2012/05/31 by Matthias R. Gaberdiel, Rajesh Gopakumar · 8 citations
Mathematics · Physics and Astronomy · #Analytic continuation #Black Holes and Theoretical Physics #Central charge #Charge (physics) #Conformal map #Cosmology and Gravitation Theories #Duality (order theory) #Equivalence (formal languages) #Geometry #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Minimal model #Minimal models #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scalar (mathematics) #Symmetry (geometry) #Triality #hep-th
paper · pdf · doi:10.1007/jhep07(2012)127
29 pages; v2. Typos corrected
openalex publication_date 2012/07/01 · arxiv created 2013/03/11 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.