Logarithmic extensions of minimal models: Characters and modular transformations
Abstract
We study logarithmic conformal field models that extend the (p,q) Virasoro minimal models. For coprime positive integers p and q, the model is defined as the kernel of the two minimalmodel screening operators. We identify the field content, construct the Walgebra W that is the model symmetry (the maximal local algebra in the kernel), describe its irreducible modules, and find their characters. We then derive the SL(2,Z)representation on the space of torus amplitudes and study its properties. From the action of the screenings, we also identify the quantum group that is KazhdanLusztigdual to the logarithmic model.
 Publication:

Nuclear Physics B
 Pub Date:
 November 2006
 DOI:
 10.1016/j.nuclphysb.2006.09.019
 arXiv:
 arXiv:hepth/0606196
 Bibcode:
 2006NuPhB.757..303F
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 43pp., AMSLaTeX++. V3: Some explanatory comments added, notational inaccuracies corrected, references added