2021/09/30 by Yifei He, Hubert Saleur
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Algorithm #Artificial intelligence #Black Holes and Theoretical Physics #Central charge #Charge (physics) #Combinatorics #Computer science #Conformal field theory #Conformal map #Conformal symmetry #Database #Duality (order theory) #Field (mathematics) #Identity (music) #Limit (mathematics) #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Physics of Superconductivity and Magnetism #Potts model #Primary field #Pure mathematics #Quantum mechanics #Rank (graph theory) #Tensor (intrinsic definition) #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.21468/scipostphys.12.3.100
published as SciPost Phys. 12, 100 (2022) · 24 pages. v2: comments added, typos corrected. v3: comments in footnote 7 improved
arxiv created 2022/02/14 · openalex publication_date 2022/03/21 · arxiv updated 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
It has long been understood that non-trivial Conformal Field Theories (CFTs) with vanishing central charge (c=0) are logarithmic. So far however, the structure of the identity module -- the (left and right) Virasoro descendants of the identity field -- had not been elucidated beyond the stress-energy tensor T and its logarithmic partner t (the solution of the "c→ 0 catastrophe"). In this paper, we determine this structure together with the associated OPE of primary fields up to level h=h=2 for polymers and percolation CFTs. This is done by taking the c→ 0 limit of O(n) and Potts models and combining recent results from the bootstrap with arguments based on conformal invariance and self-duality. We find that the structure contains a rank-3 Jordan cell involving the field TT, and is identical for polymers and percolation. It is characterized in part by the common value of a non-chiral logarithmic coupling a0=-25\over 48.