2007/02/28 by Mihály Weiner · 5 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Central charge #Charge (physics) #Combinatorics #Conformal map #Domain (mathematical analysis) #Energy (signal processing) #Geometry #Irreducible representation #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Statistics #Value (mathematics) #math-ph #math.FA #math.MP #math.RT
paper · pdf · doi:10.1007/s00220-007-0324-1
published in Communications in Mathematical Physics 277(2), 555-571 (Springer Science+Business Media) · 21 pages, no figures. V2: minor corrections
arxiv created 2007/03/01 · openalex publication_date 2007/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let Gn ⊂ \rm Diff+(S1) be the stabilizer of n given points of S1. How much information do we lose if we restrict a positive energy representation Uch associated to an admissible pair (c,h) of the central charge and lowest energy, to the subgroup Gn? The question, and a part of the answer originate in chiral conformal QFT. The value of c can be easily ``recovered'' from such a restriction; the hard question concerns the value of h. If c≤ 1, then there is no loss of information, and accordingly, all of these restrictions are irreducible. In this work it is shown that Uch|Gn is always irreducible for n=1, and if h=0, it is irreducible at least up to n≤ 3. Moreover, an example is given for certain values c>1 and h,h>0 such that Uch|G1≃ Uc_h|G1. It follows that for these values Uch|Gn cannot be irreducible for n≥ 2. For further values of c,h and n, the question is left open. Nevertheless, the example already shows, that in general, local and global intertwiners in a QFT model may not be equivalent.