Radford, Drinfeld and Cardy boundary states in the (1,p) logarithmic conformal field models

2007/11/30 by Azat M. Gainutdinov, A. M. Gainutdinov, I. Yu. Tipunin · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Amplitude #Basis (linear algebra) #Boundary (topology) #Conformal field theory #Conformal map #Context (archaeology) #Geometry #Integer (computer science) #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Space (punctuation) #Structure constants #Torus #hep-th #math.QA

paper · pdf · doi:10.1088/1751-8113/42/31/315207

published as J.Phys.A42:315207,2009 · 32 pages; minor changes, corrected typos

arxiv created 2009/02/16 · openalex publication_date 2009/07/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

We introduce ( p − 1) pseudocharacters in the space of (1, p ) model vacuum torus amplitudes to complete the distinguished basis in the 2 p -dimensional fusion algebra to a basis in the whole (3 p − 1)-dimensional space of torus amplitudes, and the structure constants in this basis are (not necessarily non-negative) integer numbers. We obtain a generalized Verlinde formula that gives these structure constants. In the context of theories with boundaries, we identify the space of vacuum torus amplitudes with the space of Ishibashi states. Then, we propose (3 p − 1) boundary states satisfying the Cardy condition.

Citations

• Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, Part I
• On Verlinde-Like Formulas in c_p,1 Logarithmic Conformal Field Theories
• The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity
• A note on the logarithmic (p,p') fusion
• Boundary states in c=−2 logarithmic conformal field theory
• Boundary states in boundary logarithmic CFT
• Critical percolation in finite geometries
• Boundary states and symplectic fermions
• Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center
• The logarithmic triplet theory with boundary
• BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY
• Modular invariance of vertex operator algebras satisfying C₂-cofiniteness

Cited by

• Kazhdan–Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models
• Lattice W-algebras and logarithmic CFTs