2001/10/31 by J. Fuchs, Jürgen Fuchs, Ingo Runkel +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Boundary (topology) #Boundary conformal field theory #Conformal field theory #Conformal map #Frobenius algebra #Geometry #Integrable system #Mathematical analysis #Mathematics #Morita equivalence #Pure mathematics #Tensor product #hep-th
paper · pdf · doi:10.1016/s0550-3213(01)00638-1
published as Nucl.Phys. B624 (2002) 452-468 · 17 pages, LaTeX2e; v2: more references and Note added in proof
arxiv created 2001/12/13 · openalex publication_date 2002/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We formulate two-dimensional rational conformal field theory as a natural generalization of two-dimensional lattice topological field theory. To this end we lift various structures from complex vector spaces to modular tensor categories. The central ingredient is a special Frobenius algebra object A in the modular category that encodes the Moore-Seiberg data of the underlying chiral CFT. Just like for lattice TFTs, this algebra is itself not an observable quantity. Rather, Morita equivalent algebras give rise to equivalent theories. Morita equivalence also allows for a simple understanding of T-duality. We present a construction of correlators, based on a triangulation of the world sheet, that generalizes the one in lattice TFTs. These correlators are modular invariant and satisfy factorization rules. The construction works for arbitrary orientable world sheets, in particular for surfaces with boundary. Boundary conditions correspond to representations of the algebra A. The partition functions on the torus and on the annulus provide modular invariants and NIM-reps of the fusion rules, respectively.