The Verlinde formula in logarithmic CFT

30th International Colloquium on Group Theoretical Methods in Physics

Ridout, David^1,2 ; Wood, Simon^1,2

Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Acton

ACT

2600, Australia^1

Mathematical Sciences Institute, Australian National University, Acton

ACT

2600, Australia^2

关键词: Conformal field theories;    Fusion coefficients;    Fusion rule;    Logarithmic models;    S-transformation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012065/pdf
DOI  :  10.1088/1742-6596/597/1/012065

来源: IOP

【 摘 要 】

In rational conformal field theory, the Verlinde formula computes the fusion coefficients from the modular S-transformations of the characters of the chiral algebra's representations. Generalising this formula to logarithmic models has proven rather difficult for a variety of reasons. Here, a recently proposed formalism [1] for the modular properties of certain classes of logarithmic theories is reviewed, and refined, using simple examples. A formalism addressing fusion rules in simple current extensions is also reviewed as a means to tackle logarithmic theories to which the proposed modular formalism does not directly apply.